The letter outlined Brooks' response to a request from Coulson that their relationship needed to end.
Despite the fact that the affair was apparently over and the discussion of agreed new "rules" for the future, Brooks nevertheless openly declared her love for Coulson and admitted she was worried about how she would cope without him.
She wrote: "The fact is you are my very best friend. I tell you everything, I confide in you, I seek your advice, I love you, care about you, worry about you.
"We laugh and cry together ... in fact without our relationship in my life, I am really not sure how I will cope. I'm frightened to be without you."
Brooks edited the News of the World between 2000 and 2003, when she left to edit the Sun. Coulson, who had been her deputy at the NOTW, then moved into the editor's chair.
Brooks married actor Ross Kemp in 2002, while Coulson and his wife, Eloise, were married in 2000. Edis explained to the jury that he was not deliberately intruding on their private lives, or making a moral judgment on their behaviour. Instead, he said, the key issue about the relationship concerned the criminal charges they both faced.
"[They] are charged with conspiracy and, when people are charged with conspiracy, the first question a jury has to answer is how well did they know each other? How much did they trust each other?
"And the fact that they were in this relationship, which was a secret, means that they trusted each other quite a lot with at least that secret, and that's why we are telling you about it."
Brooks and Coulson, along with the former managing editor of the NOTW Stuart Kuttner, and the paper's former news editor Ian Edmondson, are charged with conspiracy to illegally intercept mobile phone messages.
The charge against them relates to the period from October 2000 to August 2006. Three other former NOTW newsdesk journalists, Neville Thurlbeck, Greg Miskiw and James Weatherup, have already pleaded guilty to the conspiracy charge.
Eight defendants in the trial, which is expected to last until Easter, are facing a total of seven counts involving conspiracy to hack phones, conspiracy to pervert the course of justice, and making corrupt payments to public officials. Not all of the defendants face the same charges and all have pleaded not guilty.
The disclosure of the Coulson-Brooks affair came as the prosecution outlined the evidence it intends to present concerning the hacking of murdered schoolgirl Milly Dowler's phone. Glenn Mulcaire, the specialist investigator tasked by the NOTW to access private voicemails, pleaded guilty at an earlier stage of the proceedings to hacking her phone in 2002.
Edis said if it was proved that Kuttner, Brooks or Coulson were involved in the commissioning of Mulcaire at that time, "then that is enough to convict them [on the conspiracy to hack charge]". He told the jury: "This is important."
Edis told the jury that Brooks knew about the "practice" of phone hacking, saying she was heard in 2010 to say that it was, in the late 1990s, "widespread across the whole newspaper industry" and that "no one thought it was wrong at that time".
He said the jury would be told how, at a lunch in the northern autumn of 2005, Brooks revealed to Eimear Cook, the former wife of golfer Colin Montgomerie, that hacking was a simple process and required only the person's mobile phone number and a factory pin code.
Edis said Cook had been given an example by Brooks of a story "that had come from phone hacking" that related to Sir Paul McCartney, his ex- wife Heather Mills and an engagement ring. In 2002 the NOTW published an article about the couple headlined: "Macca throws Heather's ring out of hotel window. Exclusive."
Edis said if Cook was right "that was an account by Mrs Brooks of that story during her editorship having being produced by phone hacking".
- Independent
