You can use a workaround by copy-pasting FileA.txt to MS Word FileA.doc and FileB.txt to MS Word FileB.doc.
Then, go to Review Menu and Click Compare. In the Compare Window, just select FileA.doc as original document and select FileB.doc as revised document. Click OK.
MS Word will highlight the differerences/changes/inserted words in both documents.
Delete all lines from FileA.doc that are already present in FileB.doc.
Copy all text in FileA.doc. Paste back/replace/update to Notepad in FileA.txt.
You can also eliminate the copy-pasting from txt to doc, as you can also proceed directly to MS Word and Compare txt files (in the Compare window, just click the folder open icon and change file type from doc to txt). But save as first so that the original txt files will serve as backup in case you accidentally delete wrong lines/infos.