Recently Brownawell and the second author proved a "non-degenerate" case of
the (unproved) "Zilber Nullstellensatz" in connexion with "Strong Exponential
Closure". Here we treat some significant new cases. In particular these settle
completely the problem of solving polynomial-exponential equations in two
complex variables. The methods of proof are also new, as is the consequence,
for example, that there are infinitely many complex z with ez+e1/z=1.Comment: 26 page