Fusing E-strings to heterotic strings: E plus E → H

E-strings arise from M2 branes suspended between an M5 brane and an M9 plane. In this paper we obtain explicit expressions for the elliptic genus of two E-strings using a series of string dualities. Moreover we show how this can be used to recover the elliptic genus of two E-8 x E-8 heterotic strings using the Horava-Witten realization of heterotic strings in M-theory. This involves highly nontrivial identities among Jacobi forms and is remarkable in light of the fact that E-strings are sticky and form bound states whereas heterotic strings do not form bound states.