Solution set refers to all values that could make the equation hold true. For a linear equation, there's normally one value in its solution set. However, if the linear equation contains absolute value, they may be more than one solutions.

|2x-3| = 13

Remove absolute value sign by making the absolute value equals to both positive and negative values on righ hand side. Then, two linear equations are obtained.

2x-3 = 13 or 2x-3 = -13

Solving the two equations gives

x = 8 or x =-5

Therefore,

The solution set of the equation is {-5,8}

E is the correct answer.