Does a divorce occur if a man says to his wife in a moment of anger: "You are divorced," without intending divorce, and is this wording sufficient for divorce to take place despite not explicitly saying: "You are divorced"?

There is no difference between the phrases "you are divorced" (أنت أطلقتِ) and "you are divorced" (أنتِ طالق), as both are explicit forms of divorce and do not require intention. Consequently, the wife is divorced unless the husband's anger had removed his awareness. Since the husband was aware of what he uttered, the divorce takes place. He may take his wife back before her 'iddah (waiting period) expires without a new contract. He must be careful not to be lenient with the words of divorce.