How can I find the slip speed of a slip ring induction motor without knowing the rotor speed (rated RPM)
Homework, I guess, a theoretical one which assumes ideal stator and no substantial saturation nor stray inductance effects.

The general induction motor theory tells: In that ideal case max. torque occurs at slip=R/X where R is one phase resistance (=load + rotor wire) and X=one phase rotor reactance. Actually also negative slip = -(R/X) is valid for max torque; that has meaning for generators.