You could use register_buffer for automatic handling of your constant.
class MyModule(nn.Module):
    def __init__(self):
        super(MyModule, self).__init__()
        self.exponent = nn.Parameter(torch.Tensor([1]))
        self.e = torch.Tensor([np.e]).float()
        self.register_buffer('e_const', self.e)

    def forward(self, x):
        x = x * (Variable(self.e_const).pow(self.exponent))
        return x