Genesis 18:10

And one of them said, Returning I will return to thee in the coming year; and you shall be revived, and, behold, Sarah thy wife shall have a son. And Sarah was hearkening at the door of the tent, and Ishmael stood behind her, and marked what the Angel said.

I WILL CERTAINLY RETURN UNTO THEE WHEN THE SEASON COMETH AROUND. Rashi comments, “The angel was not announcing that he would return to him, but he was speaking to him as G-d’s agent, [meaning that G-d would return]. This is similar to the verse: And the angel of the Eternal said to her [Hagar], I will multiply thy seed exceedingly., 16:10. But he [the angel] has no power to multiply, and he was therefore speaking as G-d’s agent. So also here, he spoke as G-d’s agent.”
Now the Rabbi, Note 139. found it necessary to say so because the Holy One, blessed be He, told Abraham here, At the set time I will return unto thee.. However, whether it be a reference to the angel or to the Holy One, blessed be He, we do not find it recorded that at the set time He returned. Perhaps a reference to this return is included in the expression, And the Eternal remember-ed Sarah, as He had said, and the Eternal did unto Sarah as He had spoken.
Rabbi Abraham ibn Ezra said that the verse beginning, And the Eternal said to Abraham,. means that the angel said it in the name of Him Who sent him, and he did return at the set time which he had told him, even though it is not written in Scripture.
The correct interpretation appears to me to be that [the expression, shov ashuv (I will certainly return)], is akin to the phrase, liteshuvath hashanah (at the return of the year). The verse is thus stating: “I will surely bring back to thee a time as this time, that you will be alive and Sarah your wife will have a son.” This is similar to what was said to Abraham, At this set time in the next year. The word ashuv will then be like, ‘Veshav’ (And) the Eternal your G-d (will bring back) thy captivity and have compassion upon thee and will return and gather thee. there means “and He will bring back.” Here too the word ashuv means “I will bring back a time, like the present, in which you will be alive, and in which time, in addition to your being alive, Sarah will have a son.”

כעת חיה, she would give birth at the appropriate time. The word appears in this context in Michah 5,2 כעת יולדה בן,”until she who is to bear has given birth.” It is also found describing the state of Jewish mothers giving birth as being equivalent to that of midwives. (Exodus 1,19)

והוא אחריו, the entrance to Sarah’s tent was behind the angel. This accounts for Sarah overhearing their conversation.

שוב אשוב אליך, on the anniversary of the circumcision.

והוא אחריו, the door at which Sarah stood listening was behind the angel who was speaking.

ויאמר, the senior angel, the one whom Avraham had addressed in verse 3 with the words אם נא מצאתי חן בעיניך. שוב אשוב אליך, this was the one whose task it was to tell Sarah that she would bear a son. He spoke of his return visit a year from the present time. The other two were to destroy Sodom and to rescue Lot respectively. Three angels were required as no angel is charged with more than one mission at a time. (Bereshit Rabbah 50,2)

כעת חיה, at about this time of year next year Sarah will be giving birth. We find the term חיה used to describe giving birth in Yuma 73. On the other hand, the word may also refer to a time frame, i.e. at this time next year, seeing that you will both be alive, Sarah will bear a son. G’d had spoken of למועד הזה בשנה האחרת (compare Genesis 17,21) whereas the angel expressed the same thought in the words כעת חיה. The angel did not spell out to Avraham precisely when this birth would take place, as had G’d in the previous chapter.

ושרה שומעת פתח האהל, she had been inside her tent; when she heard the voices of the angel and Avraham. She went to the entrance of her tent to overhear what was being said. Neither the angel nor Avraham saw her at the time. seeing both their backs were turned towards the entrance. This is the meaning of the words והוא אחריו, i.e. Sarah’s tent was behind the angel who was doing the talking.