What number should be added to both sides of the equation to complete the square? x^2-10=7

I must assume that you meant   X^2-10x =7.  If that is indeed the case, then:

X^2-10x =7  =>  x^2 -10x + 25 - 25 = 7, so that (x-5)^2 = 32  (Add 25, then 
                                                                                                 subtract 25)
Then x-5 = plus or minus sqrt(16)sqrt(2) = 4sqrt(2).

Then x = 5 plus or minus 4 sqrt(2) (answers)