I think the Levenshtein algorithm and the 3rd party libraries brought out for this very simple (and perhaps poorly stated?) test case are WAY overblown.
Assuming your example does not suggest the two bytes are always different at the end, I'd suggest the JDK's Arrays.mismatch( byte[], byte[] )
to find the first index where the two bytes differ.
String longer = "this is a example";
String shorter = "this is a examp";
int differencePoint = Arrays.mismatch( longer.toCharArray(), shorter.toCharArray() );
System.out.println( differencePoint );
You could now repeat the process if you suspect the second character is further along in the String.
Or, if as you suggest in your example the two characters are together, there is nothing further to do. Your answer then would be:
System.out.println( longer.charAt( differencePoint ) );
System.out.println( longer.charAt( differencePoint + 1 ) );
If your string contains characters outside of the Basic Multilingual Plane - for example emoji - then you have to use a different technique. For example,
String a = "a is cuter than a .";
String b = "a is cuter than a .";
int firstDifferentChar = Arrays.mismatch( a.toCharArray(), b.toCharArray() );
int firstDifferentCodepoint = Arrays.mismatch( a.codePoints().toArray(), b.codePoints().toArray() );
System.out.println( firstDifferentChar ); // prints 22!
System.out.println( firstDifferentCodepoint ); // prints 20, which is correct.
System.out.println( a.codePoints().toArray()[ firstDifferentCodepoint ] ); // prints out 128007
System.out.println( new String( Character.toChars( 128007 ) ) ); // this prints the rabbit glyph.