What does the Pasuk mean when it writes that "Yosef could no longer restrain himself"?
Rashi: He could not bear the thought that the Egyptians should witness his brothers' embarrassment when he revealed himself to them (so he ordered them to leave).
Ramban #1 (citing the Ibn Ezra): He could not bear to wait for everyone 1 to leave of their own volition, so he announced that they should leave immediately.
Ramban #2 (citing Targum Onkelos) and Targum Yonasan: He could not hold himself back from crying before the people left.
Ramban #3: He asked the people to leave because he did not have the courage to withstand the entreaties of the people who were pleading with him to pardon Binyamin.
Moshav Zekenim (to 43:7): He initially intended to wait until Yaakov will come to Egypt and recognize him. He could not wait for this.
Rashbam: He was no longer able to put on a show and to control himself as he had done until now. 2
Seforno: Yosef no longer had the patience to see what all those present were doing before leaving, so he ordered them out immediately.
Ohr ha'Chayim: He could not wait for them to leave normally if he simply told them to leave. Therefore, he raised his voice and told all to leave immediately, rapidly.
Ha'amek Davar: "L'Chol ha'Nitzavim Alav" means due to all standing by him. We find a similar meaning also in Shemos 14:28 (like he explains there).
See 43:31.
Who were "the people who were standing beside him"?
Ramban #2: They were his servants, whom he now instructed to order everybody other than his brothers to leave the room. 1
Ha'amek Davar: Even though "Hotzi'u" implies that his servants must expel others, but they themselves need not leave, they understood that Yosef wants also them to leave. We find like this also in Sefer Shmuel, "Emor la'Na'ar v'Ya'avor Lefaneinu, va'Ya'avor" (Shmuel I 9:27), [i.e. he understood] by himself [to go away].
Why did Yosef tell everyone to leave before he revealed himself?
Ramban: He did not want the Egyptians to hear when he referred to his sale, 1 as that would have stigmatized, not only them, but him as well. It would have branded his brothers as evil men, who dealt treacherously with their brother and their father, and who knows how they would treat their king and themselves.
Da'as Zekenim (to 42:1), Hadar Zekenim (to 42:1): When the brothers made a Cherem not to reveal the sale, they imposed an oath also on Yosef (Refer to 37:33:2:1). 2
Rashi: He did not want the Egyptians to hear his brothers' shame when he reveals himself.
Ohr ha'Chayim: He needed to tell them about the sale, so they would know that he is Yosef (also see Seforno to 45:4). (Telling other matters would not prove this. They believed that he knew their names, the order of their births and many other things about them, via Nichush with his cup (refer to 43:33:1:1, 42:14:1:1*)! However, had he known that they sold their brother, surely he would have used this to support his assertion that they are Meraglim! Really, now that he revealed that he knows Leshon Ivri, it could be that he overheard them discussing the sale; they were not careful lest he hear them, for he feigned to need a translator (refer to 42:23:151:1)! Even though they discussed the sale beforehand, perhaps he understood only now, e.g. he learned Ivri while they were back in Eretz Yisrael! (PF)
Beis Hillel (Nedarim 28a) permit swearing falsely to murderers and thieves! Perhaps Yosef was stringent like Beis Shamai (PF).
Why didn't Yosef reveal his identity to his brothers, until now?
Maharal (Netzach Yisrael Ch. 34, p. 157): This was Hashem's decree. It would be a Siman for Yosef's descendants, as head of the ten tribes; they would be separated from their brethren to places unknown, until Hashem shall decide to reunite them amid much weeping. 1
Maharal: As the Navi describes in Yirmiyahu 31:8.
QUESTIONS ON RASHI
Rashi writes: "'Yosef could not hold back (l'His'apek) before all those standing before him' - [I.e.] he could not bear that Egyptians would be standing before him, who would witness his brothers' shame, as he revealed [his identity]." But the verse has not told us yet that Yosef was about to reveal himself!
Gur Aryeh: We may explain differently than Rashi does. Rather, Yosef could not bear to see his brothers' shame - at having been accused of theft.