  We construct simple exact solutions to the E10/K(E10) coset model by
exploiting its integrability. Using the known correspondences with the bosonic
sectors of maximal supergravity theories, these exact solutions translate into
exact cosmological solutions. In this way, we are able to recover some recently
discovered solutions of M-theory exhibiting phases of accelerated expansion,
or, equivalently, S-brane solutions, and thereby accommodate such solutions
within the E10/K(E10) model. We also discuss the difficulties regarding
solutions with non-vanishing (constant) curvature of the internal manifold.
