I bought Photoshop two a few years ago. I am trying to reinstall it, and I am getting an error message "Install needs to be updated." and "The developer of this app needs to update it to work with this version of macOS. Contact the developer for more information."
I don't think Photoshop (Elements) two was available for a Mac. So, you have not given us enough information to help you. What OS do you have? If you have Catalina, you would need Elements 2020. If you have Big Sur, you would need Elements 2021. If you have an earlier version of Elements, you will not be able to install it and will have to upgrade.
As a workaround, you could run latest verison of Parallels virtual machine for Mac with a Windows 10 OS. And then install the Windows version of PSE 2018. However, Parallels for Mac costs 80 Euros/year. The other workaround is to revert to Mac Mojave.
Nancy O'Shea, Product User & Community Expert Alt-Web Design & Publishing ~ Web : Print : Graphics : Media