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This paper presents an $\mathcal{E}$-derivation analogue of a result onderivations due to van den Essen, Wright and Zhao. We prove that the image of alocally finite $K$-$\mathcal{E}$-derivation of polynomial algebras in twovariables over a field $K$ of characteristic zero is a Mathieu-Zhao subspace.This result together with that of van den Essen, Wright and Zhao confirms theLFED conjecture in the case of polynomial algebras in two variables.

Images of locally finite $\mathcal{E}$-derivations of bivariate polynomial algebras