One approach:

1. Get the Cartesian equation of the plane H: ax + by +cz = d.

2. Get a parametric equation of the line found in (a): x = x(t), y = y(t), z = z(t).

3. Substitute x = x(t), y = y(t), z = z(t) into ax + by +cz = d and solve for t.

4. Substitute the value of t into x = x(t), y = y(t), z = z(t). These are the required coordinates of E.