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}]}]