Does a divorce take place when the husband says to his wife, "If you want a divorce, tell me; because I can no longer tolerate you, and I swear by Allah, if you want a divorce at this time," and she replied with "divorce me" while the husband was angry, and the conversation was in writing?

The wording mentioned is a promise of divorce, and divorce does not occur merely by promising it. So, your divorce did not occur merely by your wife asking for divorce as long as you did not divorce her. However, if you intended to swear by Allah when you wrote this phrase, then you must offer expiation for breaking an oath by Allah.