Well...
Definitely romanticized. Fairly accurate historically. Carter is a bit changed to be as much like Brandon Frasier's/ Nicolas Cage's archaeologist characters as they can get away with, to make this more interesting. Other characters are altered to be pretty eccentric to peak interest, to enrich the story.
As long as they stick to the actual history, I don't mind them taking such poetic license.
It is historically accurate so far as I said. The actual story is there. They didn't show that early on Carter really was in charge of practically everything. They kind of showed him as simply an archaeologist who lost his permit. He was actually in charge of the whole area when he lost his title, over a dispute with arrogant French tourists. They also didn't emphasize that because of his willingness to fight for his workers, they were very loyal to him. I hope that comes out.
I do feel they could have easily started with his boyhood and added a few episodes to this.
They also didn't show that for years he survived on his art, selling it to tourists. And his art was good! Find an original Howard Carter, you've got something.
Other than that...it's pretty darn good.
Added:
Wow did this go off the rails eventually. It's one thing to create a couple of characters in a historic story, for romance and intrigue, like Titanic did. It's another thing to take a real 21 year old woman, and put her in a romance with a real 48 year old guy! Libel, I would almost suspect? Are there living relatives who might be kind of offended? They've got this fantasy romance effecting decisions and outcomes of historic importance. Jack and Rose's fantasy romance didn't effect the steering of the Titanic, or other real events. They're making things happen because of this fake hook up.