let x = tens digit of the original number
y = units digit of the original number
so, original number has the value (10x + y)
When the digits of a two-digit number are reversed, the new number is 9 more than the original number ...
digits reversed (the new number) ... 10y + x
the new number is 9 more than the original number ...
10y + x = 9 + (10x + y)
sum of the digits of the original number is 11 ...
x + y = 11
you should be able to solve the problem using the last two equations.