One thing youu could try is to blow insulation into the cavities of that noisy wall by cutting holes in the top of the wall large enough to get the insulation tool inserted to blow in the insulation ...a good thick application of insulation should help deaden the sound from passing thru the wall...(I am surprised the builder didnot install insulation to begin with!). Another potential solution is to install foam board on the surface of the drywalled wall (my assumption is that it is drywalled) then cover the foam board with another layer of drywall or paneling to give it a more finishhed look. this should help also...you might consider doing both of the above suggestions if the first does not help enough. Hope this was helpful. If you dont like these ideas your original fear of tearing the drywall down to remedy thhe noise problem is you othher ulttimate recourse besides moving !