The second sentence of the problem gives the length in terms of the width. Let W = the width and let L = the length of the wall, in feet. Then the second sentence says that

L= 2W +10 (ten feet longer than twice the width)

The area of the wall A = W * L = W * (2W + 10). This is given as 28 square feet, so

28 = W * (2W + 10) = 2W^2 + 10W

To simplify, first divide both sides by 2 to get 14 = W^2 + 5W

Subtract 14 from both sides to get the quadratic equation

0 = W^2 + 5W - 14

Factor to get 0 = (W+7)*(W-2)

Therefore, either 0= W+ 7, so W = -7, or 0= W-2, so W=2

Since a width cannot be a negative number, W=2 feet. Plug into the expression for length to get

L= 2(2) + 10, or L = 14 feet