I'm new to Electrum, so sorry if this has been asked before.
Following the loss (thankfully small amount) of bitcoin, I decided to set up a cold storage electrum wallet in a newly setup Windows 10 laptop that has never been online.
I read up how to transfer bitcoins from the cold storage to broadcast.
However, how do I put bitcoins that I buy into cold storage?
You create an address with your offline wallet, transfer this address to an online device and send the address to the sender. He can then fund the address. You don't need to transfer anything "back" to the offline wallet, unless you want to spend your funds.
I've written a longer explanation that covers part of your confusion here:
https://bitcointalk.org/index.php?topic=5229700.msg53953744#msg53953744