Problem: In May 2021, Ken wants to buy a new business: a news agency. He goes to see Carmel, the owner of the local news agency. They swap email addresses, and tell each other that they will communicate by this way (using those addresses) to negotiate the sale.
On 15 May 2021, Ken emails Carmel, offering $200,000 to buy her news agency. On 16 May 2021, she replied that she would only sell it for $250,000.
Few minutes after this email is sent by Carmel, Ken is rushed to hospital, as a result of catching COVID-19. He stays in hospital for 3 days. During his time in hospital, Ken has no access to his emails. When he is discharged from the hospital, he sees Carmel's email mentioned above as well as another email Carmel sent him on 17 May 2021 in which she indicated that she changed her mind and was now willing to sell her business to Peter for $200,000.
At this point in time, have Ken and Carmel formed a valid agreement for the sale of Carmel's news agency, according to the law of contract? Please refer to any relevant legal cases and/or legislation to support your arguments, and ensure that you fully explain your answer.