In living with others, there is no such happiness as "having no differences". Short of one or both parties abandoning something about who they have been, which would be dissolving the persons, there is not much to be done for "solving the difference". If that endeavor ever succeeds, you find yourself one day saying "Oh, there never was a difference, really." It can happen. It can unhappen. It offers the constant pitfall of ceasing to see who the other is.
But always available is the suspension of false needs which permits a very good approximation of happiness: the savoring of difference.