Gotta say losing my weight has helped my back problems lately. If you done it before then you'll know what you're getting into, so hopefully you'll be able to stick with it to lose the first couple of stone, or whatever quickly.
If it were me though I'd maybe not Sole Source if I only wanted to do it for 3 weeks, it might be better to do the 790 plan, still get good results, so quicker losses than say WW and will help you in the longer term returning to your chosen diet plan.