Well I don't really know the fundamental way of solving questions of these kind but I considering the time pressure, I will use the following method

the question ask for the difference between x and y

|x-y| = difference between x and y

so simply keep y= 0

so, 2^x + 2^0 = x^2 + 0

2^x +1 = x^2

this is possible only when x= 3

Hope this helps