How to title a research paper of a problem which can have two solutions?
If it is possible (you have worked on each solution perfectly and each can be published separately), you can publish two papers each include one solution. I mean, you can publish solutions separately if (and only if) each of your solutions are perfectly developed and publishable.

However, if you have derived two separate solutions to a problem, it is not that much difficult to find a title for your paper. Here is one possible title which comes to my mind:


  Solution of problem P by means of two separate methods, S1 and S2


But, if you think the second solution is only an abstract and it is not developed enough to be mentioned in the title, you would better not to mention the second abstract idea in the title of your publication.