Known is the value of the assets, liabilities and retained earnings. Unknown is what the owners investment. What is the formula?
If you look at a common balance sheet, assets are the items listed on the left side of the page. Assets consist of items that are owned or that increase the value of a business. They can be tangible or intangible, short-term or long-term. Liabilities are the items listed in the first section of the right-hand side of the page. They are items that are owed and decrease the value of a company. They can also be tangible or intangible, short-term or long-term. To find the amount listed under Retained Earnings, subtract the liabilities from the assets. If you are talking about actual owner's investment, it will have been recorded in an account as he put it into the company.
I believe you the assets and liabilities mentioned in the question pertain to the balance sheet of a company.
A balance sheet is prepared as on any particular date, which is usually the end of an accounting period. The balance sheet has two main sides or heads of accounts, assets and liabilities. Assets, also called application of funds, refers to the all the assets owned by the company including fixed assets, current assets, accounts receivables, investments, bank and cash balance, or any other assets owned or monies payable to the company by debtors.
Liabilities, also called sources of funds, refers to all the money which the company owes to others as well as its own funds,that have been invested in the business. Fixed assets includes items like Owners original investment, retained profits, loans, accounts payable, or any other monies owed by the company. The owners funds, including the original investment and retained earnings are not really a liability as far as owner of the business is concerned. But for business it is one of the sources of funds, and therefore classified as liability.
In any balance sheet the total assets mus be exactly equal to the total liabilities. This is because whatever funds are available to the business from any source must equal the total assets employed in the company.
The question does not say so explicitly, but I believe it is stating that total total assets of the business is known. However on the other side of balance sheet the total liabilities is not known. Instead what is known is only the funds that the owner owes to others, this is equal to total liabilities (or sources of funds) minus the owners fund (which includes original investment plus retained earnings), and the retained earnings.
Since the total of balances on both the sides of a balance sheet must be equal, we can know the amount originally invested by the owners by subtracting liabilities (as given) plus retained earnings from the total assets.