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.

Ithink all of these events

Carbon monoxide is the answer: )