v0 = 10.;
d = 12.;
m = 5.5;
pot[x_] := v0 - v0*(Exp[-(x + 2)^2] + Exp[-(x - 2)^2/m]);
Plot[{0., pot[x]}, {x, -d, d}, PlotRange -> {Automatic, {-2, 10}}]
p[e_] := Sqrt[v0 - e];
sol1[e_] :=
ParametricNDSolve[{sy''[x] + sy[x]*(e - (pot[x])) == 0, sy[0] == 1,
sy'[0] == 0},
{sy}, {x, 0, d}, {e}];
u1[e_] := sy[d] /. sol1[e]; pu1[e_] := sy'[d] /. sol1[e];
one[e_] := p[e]*u1[e] + pu1[e];
FindRoot[one[e] == 0, {e, 1.}]
