Would you like it if someone else looked at your mail without permission? The Torah states to “Love one another as yourself” which means not doing to another person something you wouldn’t want done to you.
Privacy is a basic principle and law in Judaism. We all cherish our personal “space”. Invasion of privacy is as serious as stealing a person’s physical possessions.
Approximate a thousand years ago Rabbeinu Gershomdeclared a ban of excommunication (cherem) for a person who reads a letter intended for another person. I heard that Rabbi Chaim Pinchas Scheinberg, of blessed memory, ruled that this applies to email in the same manner as other correspondence.
Therefore I suggest trying to contact your friend or a different student in your class for the teacher’s number. But the mail is private and for “I” only.