Question 146922
Let x=the tens digit
And let y=the units digit
The original number is 10x+y
If the digits are reversed, the new number is 10y+x

Now we are told the following:

x+y=8--------------------------------------eq1

And

10y+x=10x+y+18-------------------------------eq2

simplifying eq2, by subtracting 10x and also y from each side:
10y-y+x-10x=10x-10x+y-y+18  collect like terms
9y-9x=18  divide each term by -9
x-y=-2------------------------------------------------eq2a

Add eq1 and eq2a:

2x=6  divide each side by 2
x=3-------------------------------the 10's digit

Substitute x=3 into eq1:

3+y=8 
y=5------------------------------the units digit

The original number is: 35
The new number is 53 which is 18 greater than 35

Hope this helps---ptaylor