To solve this problem there is a plugin called 'processing for tauDEM' now available for QGIS3. you can download it from GitHub. Just change the name of the folder to processing_taudem when adding it to your plugins folder for it to install correctly.
To allow it to run correctly you must go to 'C:\Program Files\GDAL' and copy 2 files (this folder should have been created with the installation of TauDEM- I'm running windows so not sure about others)
Paste these into 'C:\Program Files\QGIS 3.yourversionnumber\bin'
Set up TauDEM as normal as it will now be available in your providers list, but be wary of spaces in the file paths to the necessary folders. Mine did not work this way so I had to move them to
Once completed TauDEM will now run in QGIS3 but again the data you are working with can neither have spaces in the file name or the path, or you will still get the error message saying unable to create outputs.
Hope this helps someone as it was driving me nuts not being able to use the software in the new QGIS version.
This also works for QGIS 2.18. Using the old version still allows the filename and path to have spaces in it without falling over.
Again this is all tried and tested on Windows 10 so I am not entirely sure it applies to other OS running QGIS and TauDEM