Answer with Explanation:

Let the ten's digit be x.

Then, unit's digit = x + 2.

Number = 10x + (x + 2) = 11x + 2.

Sum of digits = x + (x + 2) = 2x + 2.

=> (11x + 2)(2x + 2) = 144

=>  22x2 + 26x - 140 = 0

=>  11x2 + 13x - 70 = 0

=>  (x - 2)(11x + 35) = 0

=> x = 2

Hence, required number = 11x + 2 = 24.