What is the angle between two orbits in the equatorial plane?

My orbit is in the equatorial plane. When i apply thrust in the y or x axis, it rotates around the focus or planet - see red and blue orbit in the image below. I know the the semi-major-axis and eccentricity of the ellipse before and after the thrust.

Note :- Argument of periapsis and ascending node are undefined because the inclination is zero.