Is it permissible to sell a commodity to a brother at a deferred price, then immediately sell it in the market at a lower price to meet a financial need, knowing that the first agreement was not a sham sale for resale?

What we understand from the question is that the questioner sold his device to his brother for 2500 deferred [payment]. Then the brother authorized the questioner to sell the device on his behalf for 1800 in the market so that he could benefit from the price and pay the questioner the price of the device he bought from him. There is no harm in this transaction, and it falls under Tawarruq. It is stated in Al-Rawd Al-Murabba': "And whoever needs cash, and buys something worth a hundred for more to expand [his means] with its price, there is no harm in it, and it is called the issue of Tawarruq."