If m=n, and m=2, then n will NEVER be equal to anything other than 2.
Proof:
Your first job in solving this is to take the square root of m^2, which is:
=> m^2 = mn
=> sqrt(m^2) = n
Why are you doing (m^2) - (n^2) = mn - (n^2) ?
If solving for n, you must:
a. m*m = m*n
b. divide both sides by m
m^2=mn
m = 2
m*m = m*n
m^2 OR 2*2 = 4
sqrt(4) = 2
4/2 = 2 = n
m = x = n where x is whatever value you give
If solving for m, you must:
a. m*m = m*n
b. divide both sides by n
m^2 = mn
n = 2
n*n = m*n
n^2 OR 2*2 = 4
sqrt(4) = 2
4/2 = 2 = m
n = x = m where x is whatever value you give