I am creating a worksheet that has information about accounts from day to
day. In the start of the worksheet I have the opening account information for
Day 1 and in the second column is the information from Day 2. The third
column has a formula that shows the change in balances from Day 1 to Day 2.
The formula for the change in accounts is: =IF(E2<0,(D2-E2),""). Some of the
opening account information from Day 1 does not contain any information until
Day 2 so the formula will leave those blank.

So my problem is: since new accounts do not have a previous balance to
subtract from their proceeding balance becomes negative. How can I alter this
formula: =IF(E2<0,(D2-E2),"") in order to give me the change in accounts and
still accommodate for the accounts that do not have a Day 1 balance?

First, a question / comment: the formula you're using now says "if the
account balance in E2 is not zero, subtract E2 from D2". Since it's
possible- maybe not probable, but possible- for an account to
legitimately hold a zero balance, could this be the source of a logic
error? If this is totally not possible then try this formula, which is
based on your example formula:
=IF(AND(D2<0,E2<""),D2-E2,"")

If it may be possible for accounts to legitimately hold a zero balance
and you need to consider this possibility, try this formula:
=IF(AND(D2<"",E2<""),D2-E2,"")