using algebra
n and n+2 are the integers
n*(n+2)=288
n^2+2n=288
n^2+2n-288=0
288=2*2*2*2*2*3*3=(2*2*2*2)*(2*3*3)=16*18 and 18-16=2
factor(n+18)(n-16)=0
n+18=0
n=-18
n+2=-16
this is one solution
n-16=0
n=16
n+2=18
this is another solution
as you can see, it's just a matter of factoring 288using arithmetic...√288=16.97≈1716 and 18 are the integers (as well as -16 and -18)