@Markiyan Hirnyk 

DirectSearch is a great package, thanks.  

About exact solutions: Most of the equations I have to solve have many variables and are far too big for exact solutions.  It's a pity that the built-in fsolve() function is too weak to solve a quite simple analytic example in only two variables.

@Rouben Rostamian  

The equation is

{6*exp(x+y)/(1+exp(x+y))+exp(2*y)/(1+exp(2*y)) = 2, 5*exp(2*x)/(1+exp(2*x))+2*exp(x+y)/(1+exp(x+y)) = 1}

It was visible when I first entered the question but then it disappeared.

The instructions in item 17 will appear to not work unles you also change the default format for new worksheets to "Worksheet" under the Interface tab (Maple 2015, Linux).  Also, the PDF document listed there is not accessible.