The tone of your letter will depend on two things - your illness and what it means to you and your friend.
First - let’s assume your "illness" is maybe not very serious. The tone is friendly and light and you are even able to put in a funny comment...
Sorry my friend but there’s no way I’m going to be able to get away next week for our fishing trip. I’ve just got back from the doctor’s (I went to get the results of some tests I had last week) and have been told to take things really easy for the next few months.
I seems I’ve got problems with my heart! My wife says it’s good news that I’ve got one - but really it’s come as bit of a shock to tell you the truth! According to the doctor I’ll have to go back for more tests and then they’ll know better what exactly is wrong with the old ticker, and in the meantime I have a course of tablets to take - and he recommends no heavy exertion and no excitement!
I told him I was off for a week’s fishing in France and asked what he thought. The answer was a definite NO. Seemingly sitting in the cold for hours is not the best thing to do at this moment in time- I did tell him I wouldn’t have much excitement fishing-but he said best to wait till after the hospital appointment...
On the other hand if your illness is serious, it may be a harder letter to write - and to receive. I think it's best kept factual and fairly short. Get the bad news over at the start - and acknowledge that your friend will be shocked...
I’m sorry to have to write this letter - sorry to be the bearer of bad news.
There’s no way of saying it gently - I’ve been told I’ve got cancer of the pancreas. The doctor has said that the prognosis is poor - he wouldn’t specify a time but judging by the look on his face - I don’t think I’ll be long.
We’ve been friends for so long, I wanted you to know straight away, but I couldn’t face telling you on the phone or meeting you in the pub and telling you there.
It came as a shock to me, and it’s still sinking in, so I know it’ll be the same with you. I’m giving next Saturday’s match a miss and will give you a call later on in the week.
There is a topic on Blurtit about letter writing. You'll find loads of different letters Here.
Hope these suggestions help x.