This is one of or perhaps even the last song that Ted ever wrote and recorded. He sang while playing the piano and captured it using a tape recorder in the mid 1990's. His daughter claims it would've been recorded in preparation for his last album "Äntligen På Väg" or "Finally On My Way" in 1994, a title given to represent that he was finally on his way back to writing music and feeling better in the midst of his illness.
However, because that old tape recorders did not store dates the tape would've had to have been carefully marked by Ted or conversely, marked on a box. If the latter is true, the marking may not be accurate to all the tapes in the box. It does seem peculiar too that there were so many great songs discovered in 2009 which weren't included in the album that it leads me to speculate that most of it might have been recorded after 1994, before he passed away in 1997, but it's hard to say.

Update: I found an article from Dagens Jubilar (spring 1996) where Ted talks about an upcoming album where it's mentioned that he was writing new music particularly using a synthesizer in Autumn and Winter of 1995. So all of the music demo tapes available are likely from around this time and forward.

This song recording was ever only released with new instrumental backing by her daughter and a short clip of the original during a podcast where a large portion was dubbed over by an interview. It took a good 20 hours but I managed to piece together the entire demo tape using AI to separate the vocals and instruments, a lot of checking and listening to figure out how the cover could've been modified and how it mapped to the original.
After this extensive puzzle I managed to extract Ted's voice entirely, thus what you hear in regards to his voice is 100% accurate through the entire demo tape. The piano is largely accurate but a good half has been copied and matched to his singing. The most intriguing part is that Ted's daughter modified and removed a small bit at 0:50, the original lyric should be: "And every single day, I know we're on our way, and things will turn out 'fine now i know' ". The last part had been cut out and replaced with a later section of the song.


This is how it was pieced together: https://i.imgur.com/e5hBZer.png
The upper layers are vocals, the lower is the piano and some are both.


Hopefully all the demo tapes will release in the future.

Lyrics

[Chorus]
I know there's a song to be sung every day about you and me
I know there's a poem to be written every day about you and me
I know there's a song and I know it's for good and I know it's for real this time

[Verse 1]
And every single day, I know we're on our way, and things will turn out fine now i know
And every single day, I know we're on our way, but things will be just as it should

[Chorus]
I know there's a song to be sung every day about you and me
I know there's a poem to be written every day about you and me
I know there's a song and I know it's for good and I know it's for real this time

[Verse 2]
And every single day, I know we're on our way, and things will turn out just as it should
And every single day, I know we're on our way, and things will be just as it should

[Chorus]
I know there's a song to be sung every day about you and me
I know there's a poem to be written every day about you and me
I know there's a song and I know it's for good and I know it's for real... this time

Mmmm...


Thanks to dragon_shoot98, as I used his lyrics as a template.