If a system has the following step response:

$y(t) = 1 - [A e^{(−t/T1)} + (1-A) e^{(−t/T2)}]$

and I know the values of A, T1 and T2, can I transform this to a discrete-time IIR filter analytically? If there is no analytical solution, is it possible to say how many poles/zeros the IIR filter should have?

I've done it numerically by using the Prony's method on the impulse response, but I'm hoping there is a more direct way.