I just purchased a copy of Photoshop Elements 2018 a few months ago, and I installed it. A week later, I wiped my computer due to a virus. When I went back to try to redownload photoshop, I couldn't because I had lost the box with the serial code. Is there a way I can recover my code or redownload it without the code since I registered it to my account? I still have the casings for the discs, so I could use those. Thank you for your time.
You will always need your serial number to re-install Adobe software.
Did you register the software when you bought it. Try signing into your account at adobe.com with your Adobe ID and see if it's listed there.
If you have the discs, the serial number is usually printed on the DVD sleeve.
Once you find your serial number, guard it with your life in case of future reinstalls. I store all my software serial numbers in a single text file in Dropbox. Has served me well for 15 years.