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.
