You can use one of the free Samsung firmware update tools to download the Samsung SM-T580 stock ROM onto your computer. Once you have the firmware file on your desktop, you can flash it with the Odin flashing tool.
There are several excellent firmware upgrade tools for Samsung. If you don’t have a personal favorite already, we recommend trying SamFwTool which has a user-friendly interface and an automatic detect feature that will try to automatically understand what firmware you need so you don’t manually need to find it.
Another reliable tool is Frija. When I’m reading the XDA Developers forum, I often come across custom firmware and root users who talk about Frija. It’s very popular among those who customize Android. It doesn’t have anything to do with customizing Android, but those who do customize Android often know the operating system and devices very well. Frija also has the auto-detect feature that will try to automatically detect which model number and region your device is so you don’t have to find that out yourself before the firmware will download.
There is also plenty of custom firmware available for the Samsung SM-T580 tablet if you have had enough of the stock firmware. Often you can find more recent firmware versions in the custom firmware section.