<apex:page id="Registration" showHeader="false" controller="SolutionLibraryTabController"  title="Solution Library" standardStylesheets="false">
    <style>
        .activeTab {background-color: #236FBD; color:white; background-image:none}
        .inactiveTab { background-color: lightgrey; color:black; background-image:none}
    </style>
    <apex:tabPanel switchType="client" tabClass="activeTab"  inactiveTabClass="inactiveTab" value="{!var}" >
        <apex:tab label="Search" name="srch" id="srch" onclick="setActiveTab('srch')">
            <apex:include pageName="SolutionLibrarySearch"/>
        </apex:tab>
        <apex:tab label="Insert" name="insrt" id="insrt" onclick="setActiveTab('insrt')">
            <apex:include pageName="SolutionLibraryInsert"/>
        </apex:tab>
    </apex:tabPanel>
    <apex:form>
        <apex:actionFunction name='setActiveTab' action='{!setActiveTab}' reRender="none">
            <apex:param id='tabname'  assignTo="{!var}" value=""/>
        </apex:actionFunction>
    </apex:form>
</apex:page>

public class SolutionLibraryTabController {
    /*Tab var*/
    public String var{get;set;}

    public SolutionLibraryTabController(){
        var = 'srch';
    }

    public PageReference setActiveTab() {
        if(var=='srch'){
            var='insrt';
        }
        else {
            var = 'srch';
        }
        return null;
    }
}

<apex:page id="Registration" showHeader="false" controller="SolutionLibraryTabController"  title="Solution Library" standardStylesheets="false">
    <style>
        .activeTab {background-color: #236FBD; color:white; background-image:none}
        .inactiveTab { background-color: lightgrey; color:black; background-image:none}
    </style>
    <apex:tabPanel tabClass="activeTab"  id="tabpanelId" inactiveTabClass="inactiveTab" value="{!var}" selectedTab="{!var}">
        <apex:tab label="Search" name="srch" id="srch" onclick="setActiveTab('srch')">
            <apex:include pageName="SolutionLibrarySearch"/>
        </apex:tab>
        <apex:tab label="Insert" name="insrt" id="insrt" onclick="setActiveTab('insrt')">
            <apex:include pageName="SolutionLibraryInsert"/>
        </apex:tab>
    </apex:tabPanel>
    <apex:form >
        <apex:actionFunction name="setActiveTab" action="{!setActiveTab}" reRender="tabpanelId,values">
            <apex:param id="tabname"  assignTo="{!var}" value=""/>
        </apex:actionFunction>

        <apex:outputPanel id="values">
            <apex:outputText value="{!var}" label="You have selected:" />
    </apex:outputPanel>
    </apex:form>
</apex:page>

<apex:page id="Registration" showHeader="false" controller="SolutionLibraryTabController"  title="Solution Library" standardStylesheets="false">

    <style>
        .activeTab {background-color: #236FBD; color:white; background-image:none}
        .inactiveTab { background-color: lightgrey; color:black; background-image:none}
    </style>

    <apex:tabPanel switchType="client" tabClass="activeTab"  inactiveTabClass="inactiveTab" value="{!var}" >
        <apex:tab label="Search" name="srch" id="srch" ontableave="setActiveTab();" >
            <apex:include pageName="SolutionLibrarySearch"/>
        </apex:tab>
        <apex:tab label="Insert" name="insrt" id="insrt" ontableave="setActiveTab();" >
            <apex:include pageName="SolutionLibraryInsert"/>
        </apex:tab>
    </apex:tabPanel>

    <apex:form >
        <apex:actionFunction name="setActiveTab" action="{!setActiveTab}" reRender="none" />
    </apex:form>

</apex:page>

public class SolutionLibraryTabController {
    /*Tab var*/
    public String var{get;set;}

    public SolutionLibraryTabController(){
        var = 'srch';
    }

    public PageReference setActiveTab() {
        if(var=='srch'){
            var='insrt';
        }
        else {
            var = 'srch';
        }
        System.debug('var  '+var);//Use debug to check if value is there
        return null;
    }
}