Here's what's likely happening and what you should do:
* Transmission Cooler Leak: The most probable cause is a leak in the transmission cooler lines, the cooler itself (within the radiator), or a crack in the radiator itself. The transmission fluid is likely entering the cooling system through this breach. Driving with this problem will severely damage both your transmission and engine.
* Don't Drive the Car: This is crucial. Continuing to drive will cause catastrophic engine and transmission damage, leading to very costly repairs.
* Immediate Action: Have the vehicle towed to a qualified mechanic or repair shop specializing in transmissions. They will need to diagnose the exact source of the leak and perform the necessary repairs. This will likely involve replacing the radiator and possibly transmission cooler lines, depending on the location of the leak. They may also need to flush the cooling system to remove all traces of transmission fluid.
* Possible Causes (Beyond the Cooler): While less likely, there's a minuscule chance of a cracked engine block or head gasket allowing fluid to mix, but the transmission fluid in the radiator points strongly towards the transmission cooler.
Ignoring this problem will lead to significantly higher repair costs down the line. Get it towed immediately to prevent further damage.