  We define an EPR-like uncertainty by using the Duan et al.'s inequality which
gives a necessary and sufficient condition for the separability of any two-mode
Gaussian state. We show that for a given amount of entanglement, the
uncertainty is minimized by pure two-mode squeezed states. Using this fact, we
write the optimal pure-state decomposition and derive a compact form for the
entanglement of formation of two-mode Gaussian states. For illustration
purposes, we consider symmetric and squeezed thermal states as special cases
and evaluate their entanglement of formation explicitly. For the symmetric
states, our result is in agreement with the Giedke et al.'s one. To our
knowledge, our work is the first one which gives the exact entanglement of
formation of two-mode squeezed thermal states explicitly.
