Question

When the digits of a two-digit number are switched, the resulting number is 18 less than the original. If the sum of the digits in the number is 12, find both numbers.

Need two equations and please solve!

It already provided one equation. Which is:

x + y = 12

Answer 1

75 is your number. When switched, it becomes 57, which is 18 less than the original. The two digits are 7 and 5, which equal twelve.
Your second equation should be:
a-12=b, with "a" being your non-switched number and "b" being your switched number

Answer 2

Lets make x one of the digits and y equal to the other digit. I think you can make the equation (10x+y)-18=(10y+x) which could be written as 9x-9y=18 and then you can divide both sides by 9 to get x-y=2
Now you have the system of equations:
x+y=12
x-y=2
2x=10
x=5
then you can solve for y using the equation x+y=12 to get y=7
Therefore the two numbers are 57 and 75.

I hope this helps. Let me know if anything is unclear.