How can the oath of divorce that states, "My wife is divorced if she speaks to or visits this friend," be annulled before the wife travels to Egypt, given that the oath was not made in a state of anger and the husband was aware of what he said?

If you made your wife's divorce conditional on her visiting her friend or speaking with her, then if that does not happen, the divorce does not occur. However, if the speaking or visiting does occur, then the divorce takes place according to the majority of scholars, in contrast to Ibn Taymiyyah, who holds that an expiation for an oath is due if divorce was not intended. A conditional divorce cannot be revoked, and the way out is to avoid the fulfillment of the condition, taking into account the intention of the one who swore the oath. If the divorce occurs, you can take her back before the 'iddah (waiting period) expires, provided it is not the third divorce, or with a new contract after the 'iddah expires.