What is the point of tangency – no calculus, please

Problem

Two lines intersect the graph . The secant line intersects the graph at point A and B and the tangent line which is parallel to the secant, touches the graph at point E. You can read the coordinates of A and B from the graph but not E. What are the coordinates of E? What are the equations of the two lines?

You can use calculus, that is, the derivative but this is a Year 9-10 problem. So, please solve it using the mathematics at these levels.

Happy Solving!!!

Hint: Application of Discriminant