The sum of the digits of a two-digit number is 16. if the digits are reversed, the new number is 18 less than the original number. find the original number.

Equation
Let one digit be x
Let the other digit = y

x + y = 16
Let the original number = 10x + y
Let the reverse number = 10y + x

10x + y - 18 = 10y + x

Comment
Bring the letters to the left and the number 18 to the right.
10x - x + y - 10y = 18      Combine like terms.
9x - 9y = 18                     Divide both sides by 9
x - y = 2

Set up a set of equations and add.
x + y = 16
x - y = 2  Now add
2x = 18   Divide by 2
x = 18/2
x = 9

x + y = 16
9 + y = 16 Subtract 9 from both sides.
y = 16 - 9
y = 7

Check
Original number = 97 
Reversed number 79
Difference             18 and it checks.