let 'x' represent the first digit and 'y' represent the second digit

The sum of the digits of a two-digit number is 12:

x+y=12

the new number formed by reversing the digits is less than the original number by 54:

y+10x +54 = x+10y

9x+54 = 9y

we we have this system of equations:

x+y=12

9x+54=9y

solving this system we have:

x=3

y=9

the original number is 39