  It has been shown that membranes and fivebranes are wave-like or
monopole-like solutions in some higher dimensional theory. Here the picture is
completed by combining the wave and monopole solutions into a single solution
of Exceptional Field Theory. This solution solves the twisted self-duality
constraint. The 1/2 BPS brane spectrum, consisting of fundamental, solitonic
and Dirichlet branes, in ten- and eleven-dimensional supergravity may all be
extracted from this single solution of Exceptional Field Theory. The solution's
properties such as the singularity structure and its asymptotic behaviour near
the core and at infinity are investigated.
