I would call a colleague to deal with the not angry customer and I would deal with angry customer. Let them say what is the problem and try to find a solution which benefits the best both the company (in long and short term, but more importantly in long term) and the customer.
If I'm alone and I have to deal with both customers then I go one by one, depending who's turn is it. If I'm already dealing with the Not Angry customer and Mr Angry barges in yelling I would tell him "Sir, if you would kindly wait for your turn. Mr and Mrs Not Angry were here first, so it only fair that I finish with them first. Then I will help you. Thank you" (you have to say Thank you so they feel like they're doing you a favour by letting you do something else which is not solving their problem)