If you sent the transaction, then you know which address you sent to.  The other address is an address in your own wallet that the change is sent back to.

If you did not send the transaction, then it is difficult to know for certain what each address is.  It's possible that thee sender sent a single transaction and paid 2 different people at the same time. It's possible that the sender sent bitcoins only to themselves moving bitcoins between wallets.  It's also possible that they sent a transaction to a single other person and that the change from the transaction was sent back to a new address in their own wallet.

Sometimes, depending on the amounts available, and the values of the outputs, it might be possible to make an educated guess as to what happened.  Sometimes that educated guess will be right, but it's always possible that the guess is wrong.

You cannot really split coins.

Let's supposed you received 1 btc from an exchange in one transaction.

If you want to send 0.1 btc to a friend you cannot split your previous 1 btc.
You will sent 1 btc, and 0.1 will be send to your friend and 0.9 btc will come back to you as a chance  usually in another address.

This is the most common type of transaction  and this is probably the case you mentioned.

As DannyHamilton mentioned, you cannot really know for sure which is the change address , but you can try to guess. For example, usually change addresses have 8 fractional digits,  while the receiver is a round number.

For example , in the above case the receiver would be 0.1 and the change would be 0.8998373 (mining fees discounted)

If there are 2 outputs, then there are 2 recipients. As simple as that and basically that's all you know.
The fact that in reality there's a high chance that one of the recipients is the same or a different address in the sender's wallet, it's only a (rather small) detail.
If you know/expect that one of the addresses is the change address, then you can look for various other small details that can provide extra info:

* if one "recipient" address starts with the same character as the sender and the other doesn't, there's a good chance that the similar address is change address

* if one address received some pretty "round" amount (in BTC, or USD, or EUR, ..) then the other one may be the change address; also because many wallets don't do fee rounding, the recipient that got coins with more number of characters after the decimal point is probably the change wallet (because of the tx fee)


All these are assumptions based on common use, but most of the times they don't really give a 100% certainty.

You almost got the name, it was "Change Address" not "Exchange Address"  

It works like that because an "unspent transaction output" (UTXO) needs to be spent whole, a part of its value can't just be deducted.
Once a UTXO was spent, it can't be used again, that's why the excess amount should be a new UTXO (the change) or it will be considered as transaction fee.
Read this: https://en.bitcoin.it/wiki/Transaction#Output

What u both say here is almost what I mean we should consider when building the UTXOs Merkle Tree or whatever data structure used.
We should make an educated guess of how long this UTXO is going to stay & maybe also put it near others likely to be spent in the same transaction.
More here on previous results showing that UTXOs maybe divided to 2-3 groups according to their lifespan, we could add ur ideas here, and also guessing/identifying burned UTXOs as they will probably live forever in the system
https://mobile.twitter.com/ArafatShymaa/status/1403246321956438017
.
This should not be hard to do, only a few if statements added to the code (after accurate analysis of all TXs kinds not just a few like I did in coinbase, accumulating rewards, distributing rewards; and what u added here gratefully enriching the idea a lot).
.
-After these few "ifs" one could think of many ways the code could branch in..

• -Two trees/forests one for long-living one for fast spending
• -Weighted tree with less weights assigned to those staying for long (to give shorter paths for the fast spent ones)
  

....
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More thoughts in here
https://mobile.twitter.com/ArafatShymaa/status/1402465971147841537