the sum of two numbers is 51 and the difference is 11.

Let the two numbers be  x  and  y:

The sum of two numbers is 51   --->   x + y  =  51

The difference is 11                  --->   x - y  =  11

Add down the columns:                    2x      =  62

Divide by 2:                                       x      =  31

Since x + y = 51 and x = 31:  31 + y = 51   --->   y = 20

The two numbers are  20  and  31.