I want to create kubernetes cluster, and what I need to do is, I have two servers. (Nodes) with 10x Intel Xeon and 32gb ram each. Can I run one application on both of them, so the application can use 20 cores, and 64gb of ram?
Of course you can't. If you run application in kubernetes, then kubernetes will create a structure called pod to help run it. Each of your server will be a node in kubernetes. The can be many pods running this application ,but for each pod it can only use the resource of one node where the pods assigned.
If your application really needs 20 cores and 64gb, then you actually need a node that has 20 cores and 64gb.
But if you just want to make the full use of the resource, you can check the resource limit of your application (or calculate it by your own) and calculate how many copies you need to fully use your resource. For example, if your application needs at least 1 core and 1gb to run, then you can use a replicas and make 20 copy(may be less).
No, it is not possible to span a single pod across 2 different physical/virtual nodes. One single application running inside your pod(minimal object in K8s) can only utilize the maximum capacity(virtually) of the underlying node on which the pod is scheduled.
As @youth Wu said, try to check the resource limit of your application and start with the minimal one and if your application really needs resources more then the available resources on a node then, you have to scale your nodes vertically without any choice.