Sometimes it is not clear. Two submissive dogs may simply run around and play. Two dominant dogs may do the same thing, but they may play rougher. As long as they are playing, it is a very good sign. But keep a watchful eye out for displays of aggression.
Some dogs are happier as the only dog in the household.
Respect your dog and his individual personality. Avoid food treats when both dogs are near as it could trigger protective instincts. When you get home, first let them off lead in your fenced yard. It will let the new dog explore the area and be less threatening to your original dog as he gets used to having the new dog around. When you bring them inside, you will have already prepared two separate eating areas, two doggie beds, etc.