What is the ruling of the Sharia on an engineer who agrees with a client on a price for a project, then delegates its completion to another engineer for a lower price, with the difference being profit for the first engineer, without the knowledge of the client or the second engineer?

There is no objection to the hired person subcontracting another to perform a task in a lease contract (ijarah) for a work that is due (fi al-dhimmah), whether for the same wage, less, or more, as long as the work does not vary depending on who performs it. This is unless the first hirer stipulated that the hired person must perform the work himself.