Oh god, this entire idea is just making me sob incoherently. Set during the episode "Fear Her". An explanation as to why the 10th Doctor did not carry the Olympic Torch.
It's before he goes back to Rose that he stops himself.
He parks the TARDIS in the backyard of the girl who was so lonely, she had to draw herself a world. The Eleventh can smell a hint of his old self, of Rose - and he heads in that direction.
He traps his Tenth self between the house and the fence, approaching immediately and without preamble. Ten freezes and they stare one another down for an instant. He has met himself before, but not quite like this. Not quite so abrupt.
The tweed coat and bow tie are immaculate. Eleven stares at his previous self, the self he so desperately wanted to keep. Loneliness has not started following him, not quite yet. There is still a spark in his eyes. "You can't go out there."
The skinny stick of a Time Lord slips his hands into his pockets. He knows. He can tell. He won't ask when or how. He simply raises an eyebrow and asks, "Why?"
"Because," Eleven's voice cracks and he swallows reflexively. Standing in the half-shadow of this house makes him nervous. He can't be seen, not now. "If you go out there, you'll run the torch and I can't let you. I can't."
"Why?" Ten insists again, eyes ablaze and lips closed, fidgeting in place. Eleven remembers this as it's happening, as it's changing. He sees what was and what is, and they are two separate things now. Time can be rewritten. It must be rewritten. For her.
"Spoilers," Eleven whispers, half to- well. All to himself. He casts his eyes downward, searching his memory for the words he has not yet heard. "There is someone who can't see you. Not out there. Not ever. If she does-"
"Then?"
"Her mind will burn and she will die."
Ten stills his fidgeting. He can't ask for a name. His future self would never give him any such information. This is as much of a warning as could ever happen. But he is crossing his own timeline for this woman, whoever she is. She must be very, very special.
"I can't let her die then, can I?"
"No," Eleven insists. He must be convincing, he knows the skepticism of his former self. "You can't let her die."
Ten pauses. Then, not really expecting to get an answer, asks, "Who is she?"
Eleven lets the memory wash over him like water in a stream.
"I was gonna be with you. Forever."
"She's my... friend. My best friend," Eleven answers honestly, forcing back the guilt. "And she'll be yours too. Someday."
Ten contemplates this, and nods slowly. "I'll go back to the TARDIS then."
Eleven nods, seeing the memories change in his mind's eye. "Rose will find you there. Don't worry."
They nod awkwardly as a goodbye and the Eleventh runs back to his TARDIS, awash with relief. It was time to interrupt the Olympics Committee in 2005 with an inventive idea for 2012.