I currently have two 10-3 leads running from two double pole 35 amp breakers in a Wadsworth 200 amp panel. One supplies the cooktop the other supplies the oven. I am going to replace the two units with a new single unit. The new unit requires a 40 amp breaker which I plan to install in place of one of the 35's. I can not run 8-3 wire from my panel to the location of the new unit. I want to know if I can safely connect the two 10-3’s parallel in a junction box, then leave the junction box with 8-3 to the new range? I plan on soldering the 10-3 ends together to prevent the wires from separating. Will the doubled 10-3's carry the 40 amp service.

No, your plan to parallel #10 wire will violate Section 310.4 of the National Electric Code 2002 Edition which stated the smallest conductor allowed to be paralleled is #1/0.

Best you can do is use a 30 Amp breaker, there is a very good chance that you will not have problems, unless you use the oven and all four burners at once.