What is the value of an 1878 E Pluribus Unum 1 dollar gold coin?

The fact that a coin has E Pluribus Unum, the national motto, on it generally wouldn't be much help in identifying it. However in this case it indicates your coin is actually a silver dollar that's been gold-plated, not a gold dollar. Actual gold $1 coins don't carry the motto because they're so small.

Unfortunately the gold plating means your coin is altered goods from a coin-collecting viewpoint. At a minimum it's still worth its silver value, about 0.77 times the current price of silver. If it's not worn or otherwise damaged it will still make a nice piece of jewelry or simply a conversation piece.