Question

in a two digit number, the sum of the digit is 8. the different between this number and the number with the digit reversed is 54, what is the number.

Answer 1

n m = 10 n + m

n+m = 8

m n = n + 10 m

n + 10 m - (10 n + m) = 54

-9 n + 9 m = 54
-n + m = 6
but
+n + m = 8
---------- add
0 +2m = 14
m = 7
n = 1
so
17

Answer 2

original:
unit digit -- x
tens digit -- 8-x
the number: 10(8-x) + x
the number reversed: 10x + (8-x)

10x + 8-x - (10(8-x) + x) = 54
10x + 8 -x - 80 + 10x - x = 54
18x = 126
x = 7
unit digit = 7
tens digit = 1

original number 17
number reversed 71

or

original number is 71
number reversed is 17

in both cases the difference between them is 54