t = 10's digit

u = 1's digit

t + u = 11

10u + t = 45 + (10t + u)

This second equation is the tricky part. It says that the VALUE of the
reversed number (10 times the unit's digit added to the ten's digit
itself) is equal to 45 more than the original number (10 times the ten's
digit added to the unit's digit)

Combine like terms: 9u - 9t = 45

Solve by elimination:

9u - 9t = 45

-9u -9t = -99

-18t = -54

t = 3, u = 8

Original number is 38.

EDIT: xjroll, I teach math for a living, so I think I should remember this. :D

Which reminds me... I'm not getting paid for this! Time to go home! :)
Asker's rating & comment
awww thxss thts what the answerr was at the end thnxss aloot i appriciatee itt ;))