To solve this problem, you want to write an expression for the length of piece of the cable. If you let x represent the length (in feet) of the shorter piece, then the length of the longer piece is 18 feet longer, so its length is x + 18.
Now you need to write an equation relating the two lengths. Since you know that the two pieces came from a 100-foot cable, the sum of their lengths must equal 100. So, you can write the equation x + (x + 18) = 100.
Finally, you need to solve the equation. Combine the two x's first to simplify the equation as 2x + 18 = 100. Subtract 18 from both sides to get 2x = 82. Divide both sides of the equation by 2 to get x = 41.
So, the shorter piece has a length of 41 feet, and the longer piece, which is 18 feet longer, must be 59 feet long. Check to see that the sum of the lengths equals 100 feet.