Yeah. I'm positive that ApexPages.currentPage().getHeaders().get('Host') fails in a Trigger because ApexPages.currentPage() has no context in a class or trigger not associated with a VF page. It will give you a nice System.NullPointerException.

ScrappyDog's suggestion looked more promising, but all it returned was NULL. Here's my code. Let me know if I'm doing anything  wrong. 

Here's what I've tried;

• String host = new ApexPages.StandardController(sol).view().getHeaders().get('Host'); returns null
• String host = pageRef.getHeaders().get('Host'); returns null
• String host = pageRef.getURL(); returns only the partial url

trigger AttachedSolutions on CaseSolution__c (after delete, after insert, after undelete,
after update) {

List<CaseSolution__c> impactingSolutions = new List<CaseSolution__c>();
List<Id> caseIds = new List<Id>();
List<Case> casesToUpdate = new List<Case>();
Map<Id, String> caseSolutions = new Map<Id, String>();

If (Trigger.isDelete || Trigger.isUnDelete) {
ImpactingSolutions = Trigger.old;
} else {
ImpactingSolutions = Trigger.new;
}

//build list of cases we need to update
for (CaseSolution__c sol : impactingSolutions) {
caseIds.add(sol.Case__c);
}

if (caseIds.size() > 0){
List<Case> updatedCases = [select Id
,KB_Solution_Title_Links__c
from Case
where Id in :caseIds
];

List<CaseSolution__c> solAttached = [select Id
,Name
,Case__c
from CaseSolution__c
where Case__c in :caseIds
];

for (CaseSolution__c sol : solAttached) {
PageReference pageRef = new PageReference('/' + sol.id);
String host = new ApexPages.StandardController(sol).view().getHeaders().get('Host'); //returns null
String Url = 'https://' + host + pageRef.getUrl();
String cseSolution = sol.Name + ' - ' + Url + '\n\n';
if (!caseSolutions.containsKey(sol.Case__c)){
caseSolutions.put(sol.Case__c,cseSolution);
} else {
cseSolution += caseSolutions.get(sol.Case__c);
caseSolutions.put(sol.Case__c,cseSolution);
}
}


for (Case cse : updatedCases){
cse.KB_Solution_Title_Links__c = caseSolutions.get(cse.Id);
casesToUpdate.add(cse);
}

update casesToUpdate;
}

}