Symmetric invariants related to representations of exceptional simple groups

We classify the finite-dimensional rational representations $V$ of the exceptional algebraic groups $G$ with $\mathfrak{g}=\mathsf{L}\mathsf{i}\mathsf{e}(G)$ such that the symmetric invariants of the semi-direct product $\mathfrak{g}⋉V$, where $V$ is an Abelian ideal, form a polynomial ring.