What can I do when I'm really angry at someone but can't immediately leave the situation?

Separate your mind from the situation. Drift into something else. Your body can sit there, but you can take your mind elsehwhere.

Try to calme down. Don't say anything that you may regret later. See things from the other person's perspective and try to make a compromise so both of you can continue your day afterwards. Even if you don't agree with the other person, try to be calm as long as you are in the same room. When you leave the room, you can let your frustration out, but not before that

Take a moment for yourself in the conversation, either while they are talking or in a conversational pause, just to think, to acknowledge and process your feelings so that your words can then express honestly and calmly how you feel - from a place that has considered what you are going to say and the impact what you say will have on you, the other person and the situation. Or if you need more time to understand and process your anger then express to the person that you're troubled or need a moment to process something that they've said, and take a moment to yourself away from that conversation to think to yourself - as long as you express this clearly to the other person then they'll understand that you're upset, that you are being mature and trying to deal with it in a thoughtful way, and they'll be given a moment to consider, process and address what they might've said that lead to this outcome.

I can recommend trying to see the situation from their perspective. Maybe they're inexperienced, vulnerable, or even unaware that their behaviour angers you. It can be hard to control your emotions like anger, but this is how you may calm down and look at the situation in a different way. Insulting them can provoke their anger and make the situation even worse than it was before, so try to avoid doing that. However, just because you are trying to understand their position, doesn't mean they are right and that you have to give way to them. Find a balance to resolve the conflict.

Know that your emotions are products of your mind, like thoughts, and that they don't have to control you. You can decide to act on them or not. Trying to control emotions can be hard and often unsuccessful, but you can accept your anger and give it space to exist in you. Recognising the emotion and being a few moments with it, listening to what it has to tell you, will free your mind for making the actions that are actually valuable for you. Breathing and mindfulness exercise can help in becoming more conscious of your emotions in that sense. The anger will not disappear, but it will not control you either.