The sum of the digits of a two digit number is 10. if the digits are reversed, the new number will be 18 more than the original number. find the number

t+u = 10

10u+t = 10t+u-54

Rearrange:

t+u=10

9t-9u=54

Simplify:

1st; t+u=10

2nd: t-u=6

Add 1st and 2nd and solve for t, as follows:

2t = 16

t = 8

Substitute in t+u=10 to solve for u:

8+u=10

u = 2

Original Number = 82