Get a lawyer to help you through this is the best way - but then you are gonna have to pay the lawyer out of the estate. I am talking about just the logistics, the lawyer isn't gonna make money appear that isn't there. OR sometimes the probate court where the deceased lived can give you some guidance.
As to your brother and the check - the estate needs to get an identifying number from the IRS - use that number to open up an estate account at a bank. But then everything needs to go thru that account - assets sold and debts paid - whatever is left, if any, is then distributed after any taxes are paid.
IRS.gov Deceased Persons – Probate, Filing Estate and Individual Returns, Paying Taxes Due
Anybody can give anything to anybody but if that anything has debt connected to it - the debt has to be satisfied before the anything that is left is given to the anybody. Just basic math (plus and minus)
Sounds like things weren't done exactly like what you thought. If you and your brother work thru this properly and lawfully with guidance you (meaning the estate) might be able to sell the house yourself but if it is not appraised at or the sell does not bring in enough to satisfy the loan - then that might be work for nothing.
If you want to keep the house, the equity loan has to be satisfied by you in order to get the security deed removed. You cannot just take over the loan. There is probably a clause that says something to the effect that it is due in full if the owners die or if they no longer live in the home. It may have been a reverse mortgage - a type of equity loan. Lots more cost and restrictions for heirs with a reverse mortage type.
Keep in mind that if the home with the (substantial) equity loan on it is foreclosed and sold, if it is brings more than what the loan is + other foreclosure cost then the proceeds should go back to the estate to pay any other debts or if none, disbursed to the heirs.
Don't go further into debt to save something that has no to little value. Perhaps your parents were using the equity loan on their home to make ends meet while they were living. It was theirs to use in that respect - perhaps they just didn't want to tell you and your brother about it.
It's Always Something . . . . Roseanna Roseannadanna