Problem:-
1-

2-

Tools:-
1-Hot Air is required.
2-Solding iron is required.
3-Skrue driver keys.
4-Electronics cleaner.
5-Four leg On of Switch ( Volume Key Switch ).
6-old board of Samsung Galaxy Tab E T560 if a few parts are damage in this board.So that they can 

Solution:-
If Volume Up or Down key is not working in Samsung Galaxy Tab E T560 then it can be the cause of Volume Switch or Resistance near by it.
So disassemble mobile phone and check whole mother board.
If there is some rust or carbon clean it with electronics cleaner and apply some heat so that it can be dry.
Check these tracks as shown in red and green lines in above diagram.
If some prints are missing or a few parts are damage apply jumpers or replace damaged parts.
If Volume Switch is damage or broken then replace it with new one.
Warnings:
Do not apply much heat it can be harm for your skin and mobile phone.
Try that board get fully dry.
When you are removing old volume switch make sure you will not damage prints from mother board so remove it when solding iron is too much hot.Or remove it with hot air.