
You will need a little bit of algebra. But stick with it, it is not difficult.

Represent the number with ABC 

Reverse this to get CBA 

Remember that A is Hundreds B is tens and C is units
Take CBA from ABC like this 

 Hundreds  Tens  Units 


 A  B  C 
   
 C  B  A 


Now here is the trick: subtract 1 Hundred, and add 9 Tens and 10 Ones (100, +90, +10 = 0, so won't change answer):
 Hundreds  Tens  Units 


 A1  B+9  C+10 
   
 C  B  A 


 A1C  9  10+CA 


Last Step: Reverse the answer and add the two numbers together.
 A1C  9  10+CA 
+    
 10+CA  9  A1C 


 9  18  9 
 (simplify:)

 10  8  9 

As predicted the answer was 1089

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