There is no ADE for any tablet.
Install the Overdrive app on your tablet. http://www.overdrive.com/software/omc/
That will let you borrow, download and read library books directly on the tablet,
with no need for a PC/Mac or ADE.
If you find it more convenient, you should be able to borrow and download books using ADE on the PC,
copy them from PC to the tablet using a file manager (eg Windows Explorer),
then read them on the tablet.
For DRM books (such as library books), the app on the tablet must be registered with the same AdobeID as ADE on the PC.
For Android and ios tablets there is also an excellent app called Bluefire for reading DRM ebooks.
For ios you cannot copy direct from PC (Apple doesn't like to make things too easy), but must use iTunes, Dropbox, email or similar.