install photoshop elements 10 without disk

You can get an external optical reader on Amazon for about $20.  But the real question is can your 10 year old software  work on the newest operating system?  

https://helpx.adobe.com/photoshop-elements/system-requirements.html#Olderversions

If you're on a Mac, no way.  Catalina doesn't support 32-bit apps.  You would need to purchase PSE 2020.

https://www.adobe.com/products/photoshop-elements.html

Try copying the disk to a flash drive on another computer with a disc drive or use an external disc drive.

For CS6 back to CS4 you may download ONLY if you bought direct from Adobe via download
-Log-in to your account and click this link https://account.adobe.com/products
--click Order history on the left and then the link to your order that will show on the right
--and finally click the link "Downloads and serial numbers" that will appear
---as always, write the serial number in a text file AND copy that text file and the
---download file(s) to an external drive (or two) to be sure you have what you need
-if you did not buy direct from Adobe via download you must find your original install
-if you have an Education or volume license you MUST use your original media
--the link for an Education or volume license download is not available at all
-if you bought a disc and don't have a drive you will need to buy an external USB drive
-if you bought and lost a disc Adobe does not provide a replacement via download
-if you bought a download from a 3rd party vendor you will need to contact that vendor

using a browser that allows popups and cookies, contact adobe support during pst business hours by clicking here and, when available, click 'chat', https://helpx.adobe.com/contact.html