Factors of 72 are (1,72), (2,36), (3,24), (4,18), (6,12), (8,9), the difference of the factors for these is 71, 34, 21, 14, 6, 1. Therefore there are no rational solutions for a and b, unless the question should have been a+b=18, in which case a and b are 6 and 12.
So we have to substitute b=a+18 in ab=72: a(a+18)=72, a^2+18a=72, a^2+18a+81=72+81.
(a+9)^2=153; a+9=±√153=±12.37, and a=12.37-9=3.37 or a=-12.37-9=-21.37. These two values give us a and b (approximately): a=3.37 and b=21.37; or a=-21.37 and b=-3.37.