Oracle doesn't have the UPDATE ... FROM syntax that you're using from MS Sql Server (which, I believe, isn't ANSI anyway). Instead, when you need to do an update on a result set, Oracle has you create the resultset as a kind of inline view, then you update through the view, like so:
UPDATE ( SELECT tp.delta_balance
, tp.post_balance
, ts.balance_due
FROM table_paid tp
JOIN table_snapshot ts
ON tp.account_no = ts.account_no
)
SET delta_balance = post_balance - balance_due;
This is more "correct" than the answers supplied by Babar and palindrom, as their queries will update every row in table_paid, even if there are no corresponding rows in table_snapshot. If there is a 1-1 correspondance, you don't need to worry, but it's safer to do it with the inline view.
It's unclear from your example which table is the parent table, or (as I'm guessing) neither is the parent table and account_no is pointing to the primary key of another table (presumably account, or "table_account" by your naming conventions). In any case, it's clear that there is not a 1-1 correspondence in your table - 15K in one, millions in the other.
This could mean 2 things: either there are many rows in table_snapshot that have no corresponding row in table_paid, or there are many rows in table_snapshot for each row in table_paid. If the latter is true, your query is impossible - you will have multiple updates for each row in table_paid, and the result will be unpredictable; how will you know which of the "post_balance - balance_due" expressions will ultimately determine the value of a given delta_balance?
If you run my query, you will find this out quickly enough - you will get an error message that says, "ORA-01779: cannot modify a column which maps to a non key-preserved table". This error will appear based not on the data in the table (it may be okay), but based on the primary keys you have defined on the two tables. If the join condition you specify doesn't unambiguously result in a 1-1 relationship between the updated table and the rest of the join, based on the defined keys, you will get this error. It's Oracle's way of telling you, "You're about to screw up your data".
In the other answers here, you will only get an error (in that case, ORA-01427: single-row subquery returns more than one row) if you actually have data that would cause a problem; my version is more strict, so it may turn out that you will need to use the other versions.
And, as the others have said, you'll definitely want an index on account_no for the table_snapshot table. One on the table_paid wouldn't hurt either.