abb1=ParametricPlot[{y E^(-y),E^y},{y,0,3},AxesLabel->{"T","m"}
,PlotPoints->100,DisplayFunction->Identity];
abb2=ParametricPlot[{x,E},{x,0,1/E},PlotStyle->Dashing[{0.01}],DisplayFunction->Identity];
abb3=ParametricPlot[{1/E,x},{x,0,E},PlotStyle->Dashing[{0.01}],DisplayFunction->Identity];
abb=Show[abb1,abb2,abb3,ImageSize->{400,300},DisplayFunction->$DisplayFunction];