It is quite likely that you don’t have time to spend on an unexpected difficult conversation or that you are not in the right frame of mind to have the conversation at that moment.
In this situation, having got over the initial emotional reaction, the best course of action is often to postpone having the conversation. It’s important to acknowledge you have heard what the other person has said and that the conversation needs to happen. The next step is to arrange a follow up conversation – and make sure that it is done. Nothing erodes trust more than agreeing to do something and then not doing it.