Let \( E: \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1, a > b \) and \( H: \frac{x^2}{A^2} - \frac{y^2}{B^2} = 1 \). Let the distance between the foci of \( E \) and the foci of \( H \) be \( 2\sqrt{3} \). If \( a - A = 2 \), and the ratio of the eccentricities of \( E \) and \( H \) is \( \frac{1}{3} \), then the sum of the lengths of their latus rectums is equal to