When you find yourself among the storm of emotion, an on-going battle of people's egos desperately trying to win, know that being still in the eye of that storm is possible.
I sometimes find myself in the midst of people's ego trips, and I have to say they amuse me. They used to get me caught up into the storm, and at times I get tempted to join the current of the ego-battle.
Keeping a mindful breath in-and-out pattern is effective when having to deal with people that come into a discussion aiming to win. You see, the ego desperately wants to win, never wants to die away to let the other 'players' on the field have a moment. It takes an unconditional/loving mindset to let go and let the storm rage on while not getting caught up in it (if you through ego-driven fuel to the fire you simply feed the beast of the storm to rage on).
The people that are driven by their ego will continue to push to 'win' the argument until they realize you are not going to contribute to the conversation until all is calm. They might continue to let off steam, but it is not them; it's their ego trying to get you involved in the egoic storm.
Once the storm passes, all that is left are two people having a conversation, and with no ego driving the conversation you can have a successful discussion.