May I know which version of Photoshop are you using and on which operating system?
I’m using Mac OS/X El Capitan, 10.11.6
Could you please elaborate what is happening when you are trying to open an image in Photoshop?
For Photoshop, take a look at this page Use the TWAIN scanner plug-in
For Lightroom, you can set up a watched folder, and use the standalone scanning software to save to that folder, and the images will be automatically imported.
For Acrobat, sorry, can't help you with that.
Generally speaking, it's IMO much better to use the standalone scanning software, and save the files to disk, then open them in Photoshop. This allows you work uninterrupted in Photoshop, without having to wait for the scanner to finish.
You could also take a look at Vuescan - a third party scanning program - which apparently has a TWAIN driver. I use Vuescan a lot, but only as standalone, so I have no experience with the TWAIN driver.