Attempting to reverse mid conversion
You can fully reconstruct L and R from M and S, as you suspect. In your case: 

$ M = {{L + R} \over 2} $

$ L = 2M - R $

$ S = {{L - R} \over 2} $

then 

$ S = {{2M - R - R} \over 2} $.

So the math checks out. Are you not getting the results you expect?

When I've worked with M&amp;S in the past, I've alyways just done the scaling by 1/2 when returning to L&amp;R. I guess it depends on what you're intending on doing with the M&amp;S signals though. If you want the sum of M and S to have equal energy to the sum of L and R, you should scale by $ 1 \over \sqrt 2 $ when converting both to and from M&amp;S.