  A supersymmetric solution to type II supergravity is constructed by
superposing two hyperk\"ahlers with torsion metrics. The solution is given by a
K\"aler with torsion metric with $SU(3)$ holonomy. The metric is embedded into
a heterotic solution obeying the Strominger system, together with a Yang-Mills
instanton obtained by the standard embedding. T dualities lead to an $SO(6)$
instanton describing a symmetry breaking from $E_8$ to $SO(10)$. The
compactification by taking a periodic array yields a supersymmetric domain wall
solution of heterotic supergravity.
