If you attach a router to the outlet on the wall, then there is only one lan socket in use on the wall. It would get split after that, at the router, which is basically the same as splitting it using a computer.
If you don't want to buy a router, that is one thing, but honestly that is the best way to do it and routers are cheap. In fact, I would not be surprised if you could get one for free (ie. freecycle, freesharing, reuseit, etc.).
Unfortunately I can not give you details on routing it through the computer as I am not familiar with your version of the OS. If that is really what you want to do, then someone else should be able to explain how to do it.