  The worldsheet theories that describe Poisson-Lie T-dualisable
$\sigma$-models on group manifolds as well as integrable $\eta$, $\lambda$ and
$\beta$-deformations provide examples of ${\cal E}$-models. Here we show how
such ${\cal E}$-models can be given an elegant target space description within
Double Field Theory by specifying explicitly generalised frame fields forming
an algebra under the generalised Lie derivative. With this framework we can
extract simple criteria for the R/R fields and the dilaton that extend the
${\cal E}$-model conditions to type II backgrounds. In particular this gives
conditions for a type II background to be Poisson-Lie T-dualisable. Our
approach gives rise to algebraic field equations for Poisson-Lie symmetric
spacetimes and provides an effective tool for their study.
