Solving inequalities

[parisse]

fsolve does not solve inequations. If I define f(x):=(1+1/x)^x-e, then f(1350.) is about -0.00100608 while f(1360.) is about -0.0009987 (beware that subtraction of 2 numbers close together will loose relative precision).
You can find an approx idea of x by doing a series expansion at infinity
series(f(x),x=inf)
and replace f(x) by the first term, -e/2x, then solve -e/2x=-1e-3