Going by your description it sounds like you're booting your Tab into its Download Mode, which you'd only need to do if you're doing something like flashing a new ROM. There's very little else to do as far as user interaction while in Download Mode.
What happens when you just restart your Tab normally, without holding down any of the buttons?
If your Tab is always booting up into Download Mode, that's not good sign -- could be the Android operating system became corrupted somehow so it simply can't boot up normally. If you have your Tab in a case, try taking it out and then restarting. If your Tab just inadvertently shifted out of place the Power and Volume buttons might have been pressed down just by accident.
If it still won't boot up normally, try booting it up into its Recovery Mode (simultaneously holding down the Volume Up, the Home, and the Power buttons). Note that while in Recovery Mode it's a text only interface so use the indicated (at the bottom of the screen) buttons to navigate through the different menu options. Select the 'wipe cache partition' option (the process should only take a few seconds), and then try to reboot normally to see if that makes any difference. See below for more detailed info:
https://www.hardreset.info/devices/samsung/samsung-t377-galaxy-tab-e-80-lte/recovery-mode/
If you can't boot up your Tab into Recovery Mode or if you can and wiping the system cache doesn't help things, try restoring your Tab using Samsung's Smart Switch utility:
https://www.samsung.com/us/smart-switch/
Smart Switch might be able to automatically restore your Tab, plus it's good to have on a computer to use as a backup utility.
But if Smart Switch isn't able to fix things, you might need to think about manually reflashing a stock Samsung ROM. This will install a clean, new OS (and new Recovery). The flashing process will require your Tab to be connected to a computer via a USB cable, a copy of the proper ROM, and and the Odin utility (a small, limited purpose utility only for Samsung devices). Go here, and get the proper ROM that matches your specific model of Tab E:
https://updato.com/firmware-archive-select-model?q=galaxy+tab+e&exact=1&r=&v=&rpp=15
Don't just randomly pick one, you need to use the ROM specific to your model I.D. ROMs are not interchangeable. Follow these directions to do the flashing process:
https://updato.com/how-to/how-to-install-an-official-samsung-stock-firmware-using-odin
-- When you use Odin, be sure to go into the Windows Task Manager and quit the Smart Switch process if it's still running in the background. Smart Switch and Odin both use the same system resources to interface between your computer and your Tab so they will conflict with each other.
-- You don't need to manually install the Samsung driver, when you did the Smart Switch install that automatically installed the latest appropriate driver.
-- Those instructions also refer to using the latest version of Odin. That might not work out in this instance as Odin has backwards compatibility issues. You might be better off just using an older version of Odin to begin with, you can get the appropriate version (matching your version of Android) from here:
https://www.droidviews.com/download-odin-tool-for-samsung-galaxy-devices-all-versions/
-- The above is based on a Windows PC. If you don't have access to one, try Heimdall, available for Linux, MacOS/OS X, and Windows. Heimdall is an Open Source alternative to Odin. Functionally it does the same thing, but there are differences in the user interface menus and such so you do need to be more flexible and what you do accordingly.
https://glassechidna.com.au/heimdall/
