Let the smaller digit = x
Then since the digits are consecutive,
the larger is 1 more than the smaller digit,
So the larger digit = x+1

That tells us that the original number is smaller than the
number with the digits interchanged.  So the original number
has the smaller first (or tens) digit.  Therefore:
The original number = 10x + (x+1)

The number with the digits reversed = 10(x+1) + x


if the digits are interchanged. the original value is increased by 9

10(x+1) + x = 10x + (x+1)

Solve that for x and what you get for x will be the smaller digit,
then add 1 to it and what you get will be the larger digit.  You
finish.

Edwin
 

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