let the two numbers be 'x' and 'y' and x be the larger that is x>y.

the larger of two numbers is 7 less than six times the smaller

x = 6*y - 7

when the smaller number is subtracted from the larger, the difference is 13

x - y = 13

by solving the system of equations

x = 6*y - 7

x - y = 13

we find

x = 17

y = 4

the two numbers are 17 and 4.