Syntax counts a bit, the Euler number is E in Mathematica or use function Exp[] as usual
Plot[x^2 - Exp[-x^2] == 0, {x, -10, 10}]
but what do you intend with it? Solving that equation symbolically would be
In[5]:= Reduce[x^2 - Exp[-x^2] == 0, x]
Out[5]= C[1] \[Element]
Integers && (x == -Sqrt[ProductLog[C[1], 1]] || x == Sqrt[ProductLog[C[1], 1]])
finding a root (there are 2) would be
In[6]:= FindRoot[x^2 - Exp[-x^2] == 0, {x, -1}]
Out[6]= {x -> -0.753089}
solving it graphically means to type
Plot[{x^2, Exp[-x^2]}, {x, -1, 0},
Epilog -> {PointSize[Large], Red,
Point[{-0.7530891649796748, (-0.7530891649796748)^2}]}]
