Let

x = the larger number

y = the smaller number

the larger of two numbers is 7 less than three times the smaller number

x = 3*y - 7

the sum of the two numbers is 53

x + y = 53

By solving the system of equations

x = 3*y - 7

x + y = 53

we find the solutions

x = 38

y = 15

The first number is 38 and the second number is 15.