R, 76 bytes

l=b=1
repeat{cat(sprintf("%*d+%d=%d
",l,T,b,s<-T+b));l=l+nchar(b)+1;T=b;b=s}

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Outputs infinitely.

If leading whitespace is allowed:

R, 74 bytes

b=1
repeat{cat(sprintf("%*d+%d=%d
",F<-F+nchar(+T)+1,T,b,s<-T+b));T=b;b=s}

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R, 76 bytes

l=b=1
repeat{cat(sprintf("%*d+%d=%d
",l,T,b,s<-T+b));l=l+nchar(b)+1;T=b;b=s}

Try it online!

Outputs infinitely.

If leading whitespace is allowed:

R, (削除) 74 (削除ここまで) 69 bytes

b=1
repeatcat(sprintf("%*d+%d=%d
",F<-F+nchar(+T)+1,T,b,b<-T+(T=b)))

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R, 76 bytes

l=b=1
repeat{cat(sprintf("%*d+%d=%d
",l,T,b,s<-T+b));l=l+nchar(b)+1;T=b;b=s}

Try it online!

Outputs infinitely.

R, 76 bytes

l=b=1
repeat{cat(sprintf("%*d+%d=%d
",l,T,b,s<-T+b));l=l+nchar(b)+1;T=b;b=s}

Try it online!

Outputs infinitely.

If leading whitespace is allowed:

R , 74 bytes

b=1
repeat{cat(sprintf("%*d+%d=%d
",F<-F+nchar(+T)+1,T,b,s<-T+b));T=b;b=s}

Try it online!