Leviticus 10:6

And Mosheh said to Aharon, and to Elasar and to Ithamar, his sons, Unbare not your heads, neither rend your garments, lest you die by the burning fire, and there be wrath upon all the congregation; but be silent and justify the judgment upon you, and let all your brethren of the house of Israel bewail the burning which the Lord hath kindled.

Do not crinify your heads Some say that this denotes growing long hair.

do not cleave your garments i.e., do not tear your garments. This word is also found in the passage “he will wear torn clothes and his hair will grow wild” [13:45]. (Some say the former adjective means “covered”; others say it means “uncovered”; but the traditional meaning is correct.)

so that you will not die “Not” takes a compound object here (compare “I have not learned knowledge, and understood holiness” [Proverbs 30:3]) as if Scripture had said “…and He not rage against the whole community”. The reason for such consequences is that the kohanim were needed to atone for the entire community.

your brethren the whole house of Israel The inclusion of Levites in the house of Israel is alluded to in the parasha of R’eh [Deuteronomy 12:17].

LET NOT THE HAIR OF YOUR HEADS GO LOOSE. “[This means]: do not grow your hair long. From this [the fact that Scripture forbade these particular mourners to let their hair grow long], we learn that a mourner is forbidden to cut his hair. [Moses thus said to them: Normally a mourner may not cut his hair], but you must not disturb the joy of G-d. THAT YE DIE NOT. But if you do this you shall die.” Thus far the language of Rashi.
Now that which Rashi says, “From this we learn that a mourner is forbidden to cut his hair,” is merely a Scriptural support for a Rabbinic enactment., p. 314, Note 449. Moreover, according to this explanation one cannot then interpret: “But if you do this [i.e., you let your hair grow long] you shall die.” Rather. But if you [the sons of Aaron] do this [i.e., let your hair grow long] you shall die” — the real explanation is as follows: “That ye die not. You need not fear death for not letting your hair grow long,” as other mourners would be so punishable if they would not let their hair grow. it was optional in the case of Aaron’s sons, Scripture stating: “You are not obliged to let your hair grow long and rend your garments, as are other mourners; that ye die not, meaning that you will not be liable to death if you do so [i.e., neither let your hair grow nor rend your garments], but other mourners are liable [to death] if they fail to observe it.” Thus also have the Rabbis said in the Gemara of Mashkin: is the name of the first chapter of the tractate. On the term Gemara see in Exodus, Seder Bo, p. 132, Note 204. “A mourner who did not let his hair grow long, and did not rent his garments, is liable [to punishment of death], as it is said, Let not the hair of your heads go loose, neither rend your clothes, that ye die not; but other mourners who do not let their hair grow long, or rend their garments, are liable [to that punishment].” But this text is similar to other Rabbinic laws for which the Talmud merely found a Scriptural support, for letting one’s hair grow long and rending one’s garments when in mourning are only matters of Rabbinic ordinance. Or perhaps the mourning of the first day [after the death and burial] is a law given to Moses at Sinai, being derived from that of aninuth [the state of mourning before the burial of a relative] according to the opinion of the Gaonim., p. 521, Note 74.
But the real meaning of the verse is an …

'ראשיכם אל תפרעו וגו, this is what Moses said to Eleazar and Ittamar, the surviving brothers of Nadav and Avihu. He told them that although they were priests and as such they were normally required to bare their heads in mourning and to rend their garments when in mourning for near relatives, on this day they had to observe the rites applicable to the High Priest for future generations, as they too had been anointed with the holy anointing oil, and the Torah gave this anointment as the reason why the High Priest could not observe rites of mourning. [remember that in the future ordinary priests would not be anointed but they acquired their status as priest through heredity from their respective fathers. Ed.]

ראשיכם אל תפרעו, even though these dead belonged to the category of near relatives for whom even priests observe mourning rites, in this instance the law was applied in its entire severity seeing that these priests had been anointed with the holy oil of anointing. The Torah had spelled this out, writing כי שמם משחת ה' עליכם, “for you (pl) have been anointed with G’d’s holy oil.” (verse 7).

כל בית ישראל יבכו, for two outstanding righteous people had been removed from them. They would therefore not be denied the eulogies due to the deceased (Sanhedrin 46)

ועל כל העדה יקצוף, “so that He will not become angry at the whole congregation;” the Lord will be angry if you display rites of mourning, as it would then appear as if your offerings which you had presented to the Lord had not been received by Him with goodwill. In the event that you would respond that if we did not mourn our brothers, the impression would be created that they had forfeited their status of being priests by what they had done, seeing that no one had mourned them, Moses commanded all the ordinary Israelites to weep and mourn for the two sons of Aaron who had been burned to death by G–d.