Proving that language is regular or not
The easiest way is to take the intersection of your language with $1^*+0=1^*$, which is
$$ \{ 1^n+0=1^n : n \geq 0 \}. $$
A similar option is to intersect with $1^*+1=10^*$, which gives
$$ \{ 1^n+1 = 10^n : n \geq 0 \}. $$
I'll let you finish the argument.