let 'x' and 'y' represent the numbers and x>y

the sum of two numbers is 7:

x + y = 7

their difference is 17:

x - y = 17

by solving the system of equations:

x + y = 7

x - y = 17

we find:

x = 12

y = -5

click here to see the step by step solution of the system of equations:

the two numbers are 12 and -5.