This is done all the time by the way with houses. Someone puts an offer out to the seller, they accept, that's it, you are under contract.
Alternatively, sellers can offer or counter offer to buyers. In this case sellers will say, here is my offer, when buyer accepts, you are under contract.
Same thing with engagement letters for professional services. Signed proposed engagement letter presented to buyer (usually with an expiration and a few outs), buyer accepts, now you have a contract.
There's been plenty of litigation in this area. If you offer $230K, the other party accepts, then you are done. You can sometimes rescind before acceptance.
Email Contract Safety Tips
Since the validity of email contracts is generally accepted under the law, it is important to exercise caution when doing business through email. To that end, the following tips may be helpful:
A contract need not be physically signed to be agreed to.
A contract may be created over a series of emails, not just one.
In some instances, a preliminary email may constitute a binding contract regardless of it referencing a future formal agreement that has yet to be agreed to.
Beware of creating an “implied-in-fact” contract, which may occur through industry custom and your conduct.
Beware of using certain terms unless you intend their meaning.
If certain conditions are desired before entering into a contract, state them clearly. Do not create the impression of a meeting of the minds if that is not the intent.
Emails however are the gotcha's. Lots of "esignature" rules mean that you don't have to actually sign an offer or acceptance anymore, but can do stuff via email. Folks DO run into trouble this way - with sometimes terrible deals agreed to via email.
Kloian v. Domino’s Pizza for a funny one where they couldn't even get a formal settlement agreement, but Domino's still forced a contract.