You probably have an "internal" coolant leak inside your engine. The coolant is escaping into the combustion chamber or crankcase through cracks in the cylinder head or block, or through a leaky head gasket.
In rare instances, coolant may also leak into the automatic transmission fluid cooler if one is located inside the radiator. But usually when automatic transmission fluid leaks into the coolant it means the line is leaking.
Pressure testing the cooling system is necessary to diagnose an internal leak. A "cylinder leak-down test" can tell a mechanic if the coolant leak is in the combustion chamber. But to pinpoint an internal leak, it is usually necessary to remove the head(s) from the engine. The head may then be pressure tested and/or checked for cracks using special equipment.
Minor internal leaks can sometimes be temporarily sealed by adding a sealer to the cooling system. But large leaks or ones that do not respond to a sealer will have to be fixed.
If the problem is a cracked head or block, repairs may or may not be possible depending on the nature of the crack. Cracks in aluminum can often be repaired by welding while those in cast iron can be fixed by pinning the damaged area. But some cracks may be so bad that they are beyond repair or in a location that makes repair impossible. In such cases, the head or block must be replaced.
If a leaky head gasket is the culprit, replacing the gasket may only temporarily cure the problem if the head or block is warped. The mating surfaces on both the head and block should be checked for flatness and resurfaced if necessary to restore flatness for a proper seal.