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Note: The phrase origins or history for particular idioms can be difficult to trace down, so finding the precise time a saying came into existance is no walk in the park. What you will usually find on this site are moments in history where an expression started to be used on a widely-known basis. For instance, some sayings can be spotted in an old newspapers from several decades ago, but think about that for a second. If an idiom is being used in a newspaper, then everybody already knows about it! What does that mean? Well, if the saying is commonly known already, then that's not where its origins are, it has to be older than that.

On that note, what's standard here is finding an early written form of the phrase, usually coming from a book, poem, play, etc., and then based on that, it gives you an idea on how old an expression could be, but not necessarily how old the idiom really is. It's an estimate. - Meanings and Origins of Phrases
Common Phrase Origins and Meanings > E-Letter Idioms
Origins for the idiom Elephant in the Room.
Ignoring an obvious problem; Failing to address an issue that stands out in a major way.
* The only functional toilet in the office was clogged and Darill's coworkers believed he was the one responsible, however, they were too embarrassed to mention it to him. Darill decided to speak up and address the elephant in the room by apologizing and admitting that he did indeed clog the toilet.

* There was an elephant in the dining room this evening when my brother sat down at the table with a black eye, but did not say anything about what had happened.
The meaning of the phrase Elephant in the Room.
The imagery for this phrase is something like this: When there's a big problem that is
easily noticeable, yet nobody is willing to discuss or even acknowledge it, then the issue
sticks out like a sore thumb. It's as if there is a giant elephant in the room and everyone
is just ignoring it despite how big and apparent it is. Seriously, you can't miss them. Elephants can grow up to 14 feet (4 m) tall and weigh up to 15,000 lb (7,000 kg).

The exact origin of this phrase is unclear, however, the phrase looks to be a relatively recent one, only being found in print as early as the mid 20th century, though it's always possible that the idiom is older. Wikipedia states that the Oxford English Dictionary credits the New York Times newspaper from June 20th, 1959, as the first recorded use of this phrase as a simile. While I am unable to find the newspaper myself to verify, there is supposedly a line from it that reads:

"Financing schools has become a problem about equal to having an elephant in the living room. It's so
big you just can't ignore it."

Reference: Wikipedia
The Letter E - Phrases starting with the letter E.
Phrases and Idioms