If I understood your post correctly, this has gone from a Thevenin equivalent question to an algebra question. To solve for R1 and R2, let's express them as some multiple of R (i.e. R1 = 5R and R2 = 7R), which is a kind of restatement of (1), but putting the unknown as a multiple of R. So, restating (2) in terms of R, 1/1000 = 1/(5R) + 1/(7R).
First: Multiply both sides by 35R
35R/1000 = 7+5 = 12
Next, Multiply both sides by 1000
35R = 12000
Now, divided both sides by 35
R = 12000/35 = apx. 342.857, or wherever you deem the need to round.
So R1 = 5R = 1714.286, and R2 = 7R = 2400.