Consider the parabola \( P: y^{2}=4kx \) and the ellipse \( E: \dfrac{x^{2}}{a^{2}}+\dfrac{y^{2}}{b^{2}}=1 \). Let the line segment joining the points of intersection of \( P \) and \( E \), be their latus rectums. If the eccentricity of \( E \) is \( e \), then \( e^{2}+2\sqrt{2} \) is equal to ________.
