Let n represent one of the numbers. Since the numbers are consecutive then let n + 1 represent the other number.

The difference of their squares equals 43. So we just need to solve the following equation.

(n +1)^2 - n^2 = 43

(n^2 + 2n +1) - n^2 = 43

2n + 1 = 43

2n = 42

n = 21

Now we can ckeck our answer.

22^2 - 21^2 = 43

484 - 441 = 43

43 = 43