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

the sum of two number is 27

x + y = 27

one number is nine less than twice the second number:

x = 2y - 9

by solving the system of equations:

x + y = 27

x = 2y - 9

we find:

x = 15

y = 12

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

the numbers are 15 and 12.