We have:\(\left\{{}\begin{matrix}a+b=11\\a.b=24\end{matrix}\right.\)\(\Rightarrow ab+a+b=35\Rightarrow ab+a+b+1=36\Rightarrow\left(a+1\right)\left(b+1\right)=36\)

We have table:(because a,b same kind so not consider a,b negative)

So the absolute difference between those two number is:\(\left|8-3\right|=\left|5\right|=5\)

We have:{a+b=11a.b=24{a+b=11a.b=24⇒ab+a+b=35⇒ab+a+b+1=36⇒(a+1)(b+1)=36⇒ab+a+b=35⇒ab+a+b+1=36⇒(a+1)(b+1)=36

We have table:(because a,b same kind so not consider a,b negative)

a+1 1 2 3 4 6 9 12 18 36
b+1 36 18 12 9 6 4 3 2 1
a 0 1 2 3 5 8 11 17 35
b 35(unsatisfactory) 17(unsatisfactory) 1(unsatisfactory) 2(unsatisfactory) 5(unsatisfactory) 3(satisfy) 2(unsatisfactory) 1(unsatisfactory) 0(unsatisfactory)

So the absolute difference between those two number is:|8−3|=|5|=5

So the answer is:

|15-2| = |2-15| = 13

||8-3| = |3-8| = 5

So the answer is 13 or 5

Tell those numbers are a,b

=> a+b = 11 and ab = 24

=> ab - a - b = 24-11 = 13

=> a(b-1) - b + 1 = 14

=> a(b-1) - (b-1) = 14

=> (a-1)(b-1) = 14

We have table:

So (a,b) = (2,15); (15,2); (3,8); (8,3)