  In this work we study the quantisation of the Seiberg-Witten curve for the
E-string theory compactified on a two-torus. We find that the resulting
operator expression belongs to the class of elliptic quantum curves. It can be
rephrased as an eigenvalue equation with eigenvectors corresponding to
co-dimension 2 defect operators and eigenvalues to co-dimension 4 Wilson
surfaces wrapping the elliptic curve, respectively. Moreover, the operator we
find is a generalised version of the van Diejen operator arising in the study
of elliptic integrable systems. Although the microscopic representation of the
co-dimension 4 defect only furnishes an $\mathrm{SO}(16)$ flavour symmetry in
the UV, we find an enhancement in the IR to representations in terms of affine
$E_8$ characters. Finally, using the Nekrasov-Shatashvili limit of the E-string
BPS partition function, we give a path integral derivation of the quantum
curve.
