Non-Riemannian Einstein-Randers metrics on $E_6\mathrm{/}{A}_4$ and $E_6\mathrm{/}{A}_1$

In this paper, we first prove that homogeneous spaces $E_6\mathrm{/}{A}_4$ and $E_6\mathrm{/}{A}_1$ admit Einstein metrics which are $Ad(T\times A_1\times A_4)$-invariant, and then show that they admit Non-Riemannian Einstein-Randers metrics.