You probably thought about this already, but the Julian way would be to dispatch on Example every time you need to use the type parameter T. For example:
julia> findparam(ex::Example{T, N}) where {T, N} = N
findparam (generic function with 1 method)
julia> x = Example(:a, [1, 2, 3])
Example{Symbol,Int64}(:a, [1, 2, 3])
julia> findparam(x)
Int64
Please don’t suggest the use of this annotation. It’s nearly always wrong, and thus actively unhelpful to mention it, then have to explain that it also causes inference to be fatally wrong. It doesn’t infer, it does the opposite: it tells inference that it’s OK to totally disregard correctness. (piever’s solution is correct).