  We show that the ring of modular forms with characters for the even
unimodular lattice of signature (2,18) is obtained from the invariant ring of
$\mathrm{Sym}(\mathrm{Sym}^8(V) \oplus \mathrm{Sym}^{12}(V))$ with respect to
the action of $\mathrm{SL}(V)$ by adding a Borcherds product of weight 132 with
one relation of weight 264, where $V$ is a 2-dimensional $\mathbb{C}$-vector
space. The proof is based on the study of the moduli space of elliptic K3
surfaces with a section.
