  Eleven dimensional supergravity compactified on $T^{10}$ admits classical
solutions describing what is known as billiard cosmology - a dynamics
expressible as an abstract (billiard) ball moving in the 10-dimensional root
space of the infinite dimensional Lie algebra E10, occasionally bouncing off
walls in that space. Unlike finite dimensional Lie algebras, E10 has negative
and zero norm roots, in addition to the positive norm roots. The walls above
are related to physical fluxes that, in turn, are related to positive norm
roots (called real roots) of E10. We propose that zero and negative norm roots,
called imaginary roots, are related to physical branes. Adding `matter' to the
billiard cosmology corresponds to adding potential terms associated to
imaginary roots. The, as yet, mysterious relation between E10 and M-theory on
$T^{10}$ can now be expanded as follows: real roots correspond to fluxes or
instantons, and imaginary roots correspond to particles and branes (in the
cases we checked). Interactions between fluxes and branes and between branes
and branes are classified according to the inner product of the corresponding
roots (again in the cases we checked). We conclude with a discussion of an
effective Hamiltonian description that captures some features of M-theory on
$T^{10}.$
