how do I resume kotfe after accidentally pressing exit arena?

go to your mission log and see if you click on the mission, there should be a play button that allows you to continue where you left off and move forward.  Make sure your not in an instance like your ship, stronghold, etc to ensure it pops up.

If that doesn't work, worse case would be to reset the mission, again make sure your not in an instance like your stronghold or ship, just do it from the fleet.