Hi there, hope not interrupting but I think you have a break in the Transmission Cooler. It functions as a cooling device for the transmission oil by circulating the oil from the gearbox to the radiator and back into the gearbox. When this device cracks or leaks, the water in the radiator and the transmission oil get mixed up. The result, u have transmission oil in the radiator which also means u have to flush all the water in the radiator and engine + flush your gearbox + transmission service. I hope its not to late to safe your engine or gearbox cause it will cost you a lot to replace them. This device must be replace with a new one every 80,000km (recommended). My friend had his e46 with same damage, cost him about Rm5k to replace his gearbox. Hope the diagram and picture helps u. Thanks guys..sorry again for interrupting.
View attachment 24989 Transmission Cooler
View attachment 24990 Transmission Cooler Diagram
View attachment 24991 Transmission Cooler connected to Radiator E60 M54
View attachment 24985 Transmission Cooler on a E46 (couldn't find yours but the diagram explains the same)
View attachment 24986 Transmission Oil in the Radiator
View attachment 24988