With EIGRP you can do equal cost or unequal cost load balancing. Variance command is used to do unequal load balancing and you don't want to use that. If you want to do equal cost load balancing the metric has to be the same. You can set the bandwidth/delay on the interfaces to be the same or use offset-list to make the metric to the same via both paths to load balance equally. If you are looking for a solution outside of EIGRP then you can use do policy routing to load balance.
Each router uses the bandwidth and delay on its own interface in the calculation of the metric. It is ideal that the bandwidth and delay should match on both ends of the connection but it is not required. To the extent that there are mis-matched values it increases the probability of assymetric routing.
There was a small confusion about what I said about variance. You can definitely using the variance command to load balance traffic across unequal paths. But I thought you were looking for a solution without using the variance command and that was the reason I said 'you don't want to use variance'.
EIGRP should proportionately load balance traffic across unequal paths based on the metric. If you want to load balance traffic across unequal links then configure the links to reflect the actual bandwidth and this way traffic will be load balanced according to the capacity of the link.
As far as your second question about bandwidth/delay configuration Rick has already provided a good explanation.
I know I repeat myself in that, but I'm still waiting (it is about 12 years now) to see a clear set of "show commands" that demonstrate that EIGRP is sharing traffic proportionally to the metric.
EDIT: I used to require the demonstration to be taken in a real production network. Since nobody even managed to do that, I would now be satisfied with a lab example, where CEF, or at worse,route-cache, is kept active and some reasonable traffic (~ 5 Kpps) is present. And to make it easier, I won't even insist on maintaining packet order !
We are pleased to announce availability of Beta software for 16.6.3. 16.6.3 will be the second rebuild on the 16.6 release train targeted towards Catalyst 9500/9400/9300/3850/3650 switching platforms. We are looking for early feedback from custome...