Looks like the radiator blew and the antifreeze is gone. See melting on rubber above radiator. Wife said there was black smoke when she got home. Does the engine need a head gasket or rebuild? Is there a test I can do?

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My Daily : 96 E-300 Diesel with 195,000 miles
Retired: 92 300D 2.5 T 345K miles and for sale
Retired: 95 E320 157K miles and currently parked with blown engine

Both retired cars are for sale as is my w124 shop inventory