When trying to resolve a conflict, you need to remain calm. Turning things into an angry screaming match will not solve problems, it will only create them.
In short, you must try and stay relaxed, and speak softly but powerfully. Be direct, and don't tippy toe around the issue. But don't be aggressively assertive, either.
Strike a balance between remaining calm, cool, and collected - along with still being up front and direct.