Using one unknown:

Let the larger number = x

>>...The sum of two numbers is 40...<<

Since 

larger number + smaller number = Sum of both numbers

Smaller number = Sum of both numbers - larger number

so

Smaller number = (40 - x)

>>,,,Their difference is 8...<<

Larger number - Smaller number = 8

                  x - (40 - x) = 8

Solve that and get x = 24

So larger number = x = 24
Smaller number = 40 - x = 40 - 24 = 16

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Using two unknowns:

Let the larger number = x

Let the smaller number = y

>>...The sum of two numbers is 40...<<

 x + y = 40

>>...Their difference is 8...<<

 x - y = 8

So we have the system of two equations in two unknowns

 x + y = 40
 x - y =  8

Can you solve that system? If not post again asking
how.

x = 24, y = 16
       
Edwin