Question 705702
Some may quickly recognize that as a product, and being a factor of 5, 13*5=65, which we may also recognize as 12*5 plus one more 5.  Basic addition fact may be in some people's heads and 8+5=13 is immediately recognized.  


You ask for "what's the number", but the description indicates TWO numbers.  I see 13 and 5.  


You probably want an algebraic arithmetic treatment so here it is.


Numbers m and n.
Differ by 8:  n-m=8
Product is 65:  mn=65
Find m and n.


The Differ equation gives n=m+8.  Use this in the Product equation.
m(m+8)=65
m^2+8m-65=0, which we can factor, so let's do that:
(m+5)(m-13) ---- will that work?  No.  Gives -8m instead of +8m.
(m-5)(m+13) ---- Will that work?  Yes.  13m-5m=8m, and product in const. term is -65.


OKAY, solution to the quadratic formed is m=5 or m=-13.  
What about n?
n-m=8
n=m+8
For m=5, n=13.
For m=-13, n=-5.


ANSWER: Both solutions fit the description.  Either the numbers are -5 and -13, or they are 5 and 13.