The background underlying the $eta$-deformed $AdS_5times S^5$ 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.
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