Is a wife divorced in a fit of anger considered irrevocably divorced, and is it permissible to take her back after that while the relationship between the spouses continues?

If you pronounced divorce while overcome and not in control of your intellect, then your divorce is not effective. However, if you were aware, your divorce has occurred even if you were in a state of extreme anger, and it is an irrevocable divorce [talaq (definition) ba'in] with no possibility of return except with a new contract, because you have not consummated the marriage with your wife nor had a valid private seclusion with her.