You should consider the basic tenets of contractual agreement, i.e. offer and acceptance. Start by analysing whether or not an offer was pronounced as opposed to an invitation to treat. (consider Gibson v Manchester City Council and Storer v Manchester City Council). Likewise, apply the case-law of an invitation to treat (Harvey v Facey would be a good starting point). State that an offer must be distinguished from an invitation to treat, by which a person does not make an offer but invites another party to do so. Back this up with academic authority - for example, Professor Treitel’s exposition of an offer is a quintessential authority in contractual theory (your textbook may have a definition of offer - be sure to correctly cite the passage with the in-text reference).State that, in order for an offer to be binding, the offeror (the person making the offer) must display a willingness to be bound as soon as it is accepted (Gibson v Manchester City Council). On the facts, it would seem that Tom's case is comparable to Storer v Manchester City Council, wherein it was held that the phrase 'if you sign and return the agreement, I will send you the agreement' compromised a valid offer.
The terms would appear sufficiently clear to express an intention to be bound as soon as it is accepted (i.e. by returning the slip) and would thus amount to an offer. Next, you need to analyse whether or not Tom's letter can amount to an acceptance. His pronouncement that he would like to join the coach at Paris and have the price reduced accordingly may constitute a counter-offer as opposed to acceptance (Hyde v Wrench). Here, you should note what a counter-offer is. Generally, where a communication requests its own terms, it represents a counter-offer; likewise, trying to negotiate the price is not a conditional acceptance, rather it is a counter-offer. Tom's lack of willingness to contract on specified terms amounts to a counter-offer. If Tom's letter is a counter-offer, you should consider acceptance. An offer must be accepted and mutual assent must be present. (Entores v Miles Far East Corp). Postal acceptance would be applicable here - the general rule is that a postal acceptance takes effect when the letter of acceptance is posted (Henthorn v Fraser) even if the letter is lost or destroyed (Adams v Lindsell). However, where the travel company did not post acceptance, it is customary that silence cannot amount to acceptance (Felthouse v Bindley). Therefore, where there is no mutual assent as to the counter-offer supplied by Tom, no contract has been formed.
Notwithstanding the lack of assent, Tom purports to send acceptance on May 19th to the original terms; however, this does not have binding effect - the counter-offer on April 30th kills the terms of the original offer as per Hyde v Wrench. Regardless of whether or not the postal rule may apply, no offer subsisted due to the counter-offer terminating the original offer.
Contract law takes an objective approach to contract intention; that is, it seeks to analyse the parties' intentions by looking at their words or actions as opposed to their psychological intention. This was defined in Smith v Hughes. You should analyse whether or not the court, when applying the objective test, could come to the conclusion that a contract had been effected. Customarily, without the basic requisites of contractual formation (mutual assent) no contract can be made. Moreover, Tom's 'acceptance' on May 19th would not have effect wherein he made a counter-offer; it is objectively clear that, where a counter-offer is made, it terminates the original offer and, therefore, cannot be accepted. The basic rule is no acceptance, = no contract (silence cannot amount to a contract).