The sum of the digits of a 2 digit number is 12 . if the new number formed by reversing the digits is greater than the original number by 18. find the original number

When we reverse the digits of a two-digit number, the difference is always divisible by 9.  
In fact, the difference DIVIDED by 9 gives the difference in the original digits.

For example, 54-45=9, 9/9=1, 5-4=1 is also 1.
Another one:  63-36 = 27, 27/9=3  which equals 6-3.

So if the difference between the number and the number with digits reversed is 18, the difference of the digits is 18/9=2

So now we know about the digits:
sum=12
difference = 2

The larger digit = (12+2)/2 =7
The smaller digit = (12-2)/2 = 5

Hence the number is either 57 or 75.

Since the original number is smaller than the one with digits reverse, the original number is 57.

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