TL/DR: Any way to work out if known numbers between a known start and ending figure should be positive or negative numbers?

I am developing an application in PHP which can import and read PDFs. The PDFs are financial ones such as bank statements with records of transactions in and out of a bank account. I only have PDFs to work with, no other formats such as CSV unfortunately.

I convert the PDF to HTML using pdftohtml and start parsing the data, the intended end result is an array of transactions. So far I have it working smoothly collecting dates, descriptions and balance. Converting the XML instead doesn't help.

There are other pieces of transcriptional data such as debit or credit amounts. In the PDF, the credit amount is in one column and the debit amount is in another column so it is quite clear in the PDF. However, when converted to HTML, the formatting is lost and therefor I don't know if the amount was a credit or debit amount.

So, my question is, given a starting balance and an ending balance and several known figures in between, is it possible for a programme to work out if those known figures in between are credit or debit amounts?

I imagine there could potentially be several combinations of those known values to reach the ending balance so I'd like to apply a formula to return the correct credit/debit sequence only if its the only possible solution. If there are several ways of adding/subtracting the known values to reach the end balance, I can ask the user to look at it manually but I'd like to keep this to a minimum if possible.

Possible to do, do you think? Thank you in advance for any help.