Solving inequalities

[parisse]

This equation can not be solved exactly, only numerically. First replace the limit with the value e then try with fsolve with an interval (for bisection).
f(x):=(1+1/x)^x;
l:=limit(f(x),x=+infinity);
fsolve(abs(l-f(x))=1e-3,x=-2000..2000)