I understand that in end to end encryption the message is encrypted and only the recipient has the key to Decrypt it. How is the key transmitted, and how can the key not get intercepted with the message?

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There are a few ways you can send encrypted information, but they all boil down to the same concept: Create a problem that is very difficult to solve unless you already know part of the answer. For example, I have a number that when divided by 7(a prime key in this case) has a remainder of 3. It could be 10, 17, 24, etc… We then take that number’s remainder, raise it to a power and multipy it by a large number to create a huge result. I send this result to the other party without sending my prime, along with the number I multiplied. They choose their own prime and do some more math with my result and send back the result. Since I know my prime, its simple for me to get the result but anyone watching would have to do a lot of math to get the answer.

Two excellent videos on the subject: https://youtu.be/NmM9HA2MQGI https://youtu.be/Yjrfm_oRO0w

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