http://pastebin.com/HBMqEnVn

BigReactors-0.4.0rc3
ThermalExpansion-[1.7.10]4.0.0B5-13
CoFHCore-[1.7.10]3.0.0B4-29

I just had this problem, so I looked into the cause. One of the classes in CoFHCore has been moved. I fixed it by hex editing CommonProxy.class in Big Reactors. I uploaded it so you can use it while waiting for an official fix: link

Edit: There's another renamed class referenced in 2 Big Reactors classes. I've hex edited those, too. The file at the link has been updated. Unfortunately, now it's giving this error:
java.lang.NoSuchFieldError: oreProxy
at erogenousbeef.bigreactors.api.registry.Reactants.getSolidToReactant(Reactants.java:232)

Same issue here. I'd post a log, but mine is nearly identical to the one posted above.

TeamCoFH @TeamCoFH · 8m
If you're using BigReactors, welp...gonna have to wait for an update to that I believe. Sorry for the API incompat, but it was on request