Transforming a delay-differential equation into an ordinary differential equation

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Is it possible to transform the following system of delay-differential equations into a system of ordinary equations:

$u_E'(t) = I_0 - u_E(t) -W_E(1 -\frac{2^4}{2^4+u_I(t-\tau)^4})$

$u_I'(t) = - u_I(t) + W_I(1 - \frac{2^4}{2^4+u_E(t-\tau)^4})$

$I_0$, $W_E$ and $W_I$ are constants.