Unfortunately there is no way for Alice or Bob to determine the individuals times A and B, without outside communication or knowledge. The best they can do is determine the value of A+B.
To illustrate why, let us first consider one approach one might take. One could allow Alice to send her time to Bob, and Bob to immediately send his time to Alice, and back and forth. In the following table I have assumed the clocks are out of synch by 8 units, and A = 2 and B = 5.
Table of Scenario 1:
A "Y(x)" in the diagram represents a signal was received, where "x" is the value of the signal received. The initial "Y" at time 0 is when Alice sends her first signal.
Now from the above table, Alice can easily deduce A+B = 7, and Bob can do the same. Now clearly there is no point in this process continuing further, because Bob can already now deduce what his next received signals will be and the times he will receive them. E.g. Y(14) at 24 seconds, then Y(21) at 31 seconds etc., and Alice can deduce what her received signals will and the times she will receive them. E.g. Y(17) at 14 seconds, then Y(24) and 21 seconds etc. So no more information can be exchanged between the pair.
Now consider the same scenario but where the clocks are out of synch by 7 units, and A = 3 and B = 4.
The following table shows the signals received and the times they are received.
Table of Scenario 2:
The important thing to notice here is that despite a difference in time synchronization and a difference in the values for A and B, the signals are all sent and received at identical times to previous example, with identical values. That is, if Alice and Bob receive signals in such a pattern, there is no way they can determine if they are in Scenario 1 or Scenario 2 or many other scenarios for that matter.
So while this isn't the only strategy Alice and Bob could attempt, it is clear that this strategy shares maximal knowledge between Alice and Bob - that is, Alice knows everything Bob knows and Bob knows everything Alice knows. Therefore no other strategy will be able to transfer additional information to derive the values of A and B individually.