Email to Case Premium exposes an Invocable Method, which is intended to be leveraged in Flow. However, this method can also be invoked via Salesforce Apex. If an external system is calling out to Salesforce, there are options for running the provided Apex code to invoke the method, such as the REST tooling API or Salesforce CLI; however, this falls outside the scope of Email to Case Premium support. This information is intended for seasoned Salesforce developers.

Email to Case Premium does not provide any endpoints for external systems, but the method can be invoked via Apex as follows:

2. Id caseId = '<id of the case to add a comment to>'; //Example: Id caseId = '500Hp00001s6SIfIAM';
   String message = 'This will be a public case comment';
    
   E2CP.InvocableSend.SendRequest sendRequest = new E2CP.InvocableSend.SendRequest();
   sendRequest.caseId = caseId;
   sendRequest.isPublic = true;
   sendRequest.body = message;
   //sendRequest.cannedResponseId = <Id of the Canned Response to use. Leave blank when specifying body.>;
   //sendRequest.templateId = <Id of the email template to use>;
   //sendRequest.fileAttachments = <List of ContentDocument ids to be included as attachments>;
   sendRequest.commentOnly = true; //Set to false if an email should be sent.
   //sendRequest.createDraft = <True if a draft should be created instead of a comment>;
   //sendRequest.scheduledSendAt = <Datetime for scheduling the response>;
   List<E2CP.InvocableSend.SendRequest> sendRequests = new List<E2CP.InvocableSend.SendRequest>{sendRequest};
    
   E2CP.InvocableSend.send(sendRequests);

Please note that the fileAttachments, commentOnly, createDraft, and scheduledSendAt parameters are only available starting in E2CP version 9.68. Older versions assume commentOnly = false.