Decoupling two signals where one is a delayed version of the other I have a signal $y(t)$ that consists of the sum of two signals where one is a time delayed version of the other.

$ y(t) = x(t) + x(t-t_{d}) $

$x(t)$ is known but the time delay $t_d$ is not.

I would be interested to know what (if any) techniques could be employed to recover the time delayed signal from $y(t)$. 

I believe for techniques such as ICA it is required to have two receivers to decouple the signals fully however neither signal would be known in advance for this case.
You can employ cross correlation of the received signal with the signal you know that is contained.

Fs = 1000;
t = np.arange(0, 2, 1./Fs)
s = lambda t: np.cos(2*np.pi*10*t*t)

t0 = 0.5

single = s(t)
signal = s(t) + s(t-t0)

plt.subplot(1,2,1)
plt.plot(t, signal)
plt.plot(t, single)

plt.subplot(1,2,2)
plt.plot(t, np.correlate(signal, single, 'same'));




The delay between the peaks is the time distance between both signals.