In Maxima predefined constants start with a % (try ??% at the prompt to check which, or simply %e,numer or %phi,numer for a couple of examples)
Se replace e by %e:
h(t):=N0*(n^4*(%e^((1-n)*t)/n^2)/(1-n)^2-(n^2/(%e^(t/n))));
in this case it is also possible - and advisable? - to replace by exp():
h(t):=N0*(n^4*(exp((1-n)*t)/n^2)/(1-n)^2-(n^2/(exp(t/n))));
Both of these should work just the same.
(edit)
You could also define e's value: e:2.718281828459045. That would be silly, but serves to point that to Maxima your e is simply a regular variable, just as much as n or N0, so it ended up assigned to an "empty" value, causing the "expression evaluates to non-numeric value" error.