Yeah they have offered the most direct answer. However, in the equation of magnitude of E-field, I cannot see the gain of the horn antenna. I wonder how this equation will relate to different antenna gain.
On slide 18 of the presentation, there is a formula for the gain of a pyramidal horn. There is also an approximation for the gain:
G = eff*4*Pi*Aph/lambda^(2). The efficiency (eff) of a horn type antenna is estimated to be between 0.75 and 0.9. Aph is the physical area of the aperture. This is a general equation for aperture type antennas.
An excellent source for antenna design is Stutzman and Thiele, "Antenna Theory and Design".