  The background underlying the $\eta$-deformed $AdS_5\times S^5$ sigma-model
is known to satisfy a generalization of the IIB supergravity equations. Their
solutions are related by T-duality to solutions of type IIA supergravity with
non-isometric linear dilaton. We show how the generalized IIB supergravity
equations can be naturally obtained from exceptional field theory. Within this
manifestly duality covariant formulation of maximal supergravity, the
generalized IIB supergravity equations emerge upon imposing on the fields a
simple Scherk-Schwarz ansatz which respects the section constraint.
