let x and y be the numbers and x>y

the larger of two numbers is 12 less than twice the smaller number

x = 2y - 12

the sum of these two numbers is 45

x + y = 45

by solving the system of equations

x = 2y - 12

x + y = 45

we find

x = 26

y = 19

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

the two numbers are 26 and 19.