Simply expand the brackets, transpose the 18 to the LHS and apply a suitable method of solution of quadratic equations. That is how we solve this (and all such) equation. Why don't you make a try?
Substitute (x - 24) with u to produce u^2 = 18.
Try factoring 18 such that one of its factors is a square. In this case: 2 x 9.
With the 2x9 clue, you can square root further 9, to produce 3. This is your whole number.
Put 2 inside a radical symbol. This produces either 3sqrt(2) or -3sqrt(2).
With the two half-answers, just add 24 to both half-answers to get 2 answers.
The answers are: {24 + 3sqrt(2),24 - 3sqrt(2)}