Hello again,
I will solve the problems step by step:
$a - b = sqrt a - sqrt b$
or, $(sqrt a - sqrt b)*(sqrt a + sqrt b) = sqrt a - sqrt b$ since $a^2 - b^2 = (a-b)(a+b)$
or, $(sqrt a + sqrt b) = 1$ this part is crucial since its given a not equal to b, so we can cancel the non-zero term $sqrt a - sqrt b$ on both sides

or, $sqrt a = 1- sqrt b$ Now squaring both terms

or,$a =(1- sqrt b)^2$
or, $a =1 + b - 2sqrt b$

So the given answer is choice C.