confused around the operation of secret profits and liability of agent?

Hunchback

I am working on problem question, and have exhausted the materials available to me but there remains one or two aspects of the problem I can't work out.
I wonder if anyone here can help?

Contract Law issue- in relation to 'agency'

Principal instructs agent to purchase on his behalf 10 specified cars from 3rd P. Agent does not disclose he is an agent to 3rd P.
Agent purchases cars as instructed, but whilst there purchases a further 2 particularly nice cars at an extremely nice price. He sells one himself and makes a handsome profit. He tells the principal about the remaining unsold car. The principal is delighted and ratifies his actions.

Issues arise, and the principal is unable to pay for any of the cars and refuses to take delivery. 3rd party wants to sue principal.

Okay, so I know that the undisclosed principal can only ratify that for which he has given express authority to the agent to purchase. I also know that in breaching his fiduciary duty, the agent will be compelled to hand over any secret profits he made.
So thats where I am confused. It seems to me the principal has to pay for the ten cars. What about other two cars? Do they form a collateral contract between A and 3P? If so, does the 3P pursue A for payment of both? Does P still get any secret profits made by A?

Also, one last thing that confused me about this question.. The agent never disclosed he was working as a principal. Yet at the end of the question, it says without explanation, that the 3P is going to sue P. Is the implication that he discovered the P in the intervening period, and that P, being satisfied with A's purchase did nothing to indicate he had acted ultra vires, which would mean he could be estopped from denying his obligations under the contract by virtue of apparent authority he gave A?

I know this is a bit of a tl;dr, hopefully there is at least one of ye that can muster the patience :cool:

Hunchback

okay, i think actually typing that question helped me work it out
there are 2 possible answers, and it depends on the communication between P and 3P from the time of contracting to the point where 3P is sueing, whether or not its agency by estoppel or the doctrine undisclosed agency!