sqlcmd issues with -E and -S flags
I just put your command into a SQL Server Agent Jobstep configured to use CmdExec; it ran the command perfectly.  

USE [msdb]
GO

/****** Object:  Job [CmdExecTest]    Script Date: 2018-03-19 10:55:07 AM ******/
BEGIN TRANSACTION
DECLARE @ReturnCode INT
SELECT @ReturnCode = 0
/****** Object:  JobCategory [[Uncategorized (Local)]]    Script Date: 2018-03-19 10:55:07 AM ******/
IF NOT EXISTS (SELECT name FROM msdb.dbo.syscategories WHERE name=N'[Uncategorized (Local)]' AND category_class=1)
BEGIN
EXEC @ReturnCode = msdb.dbo.sp_add_category @class=N'JOB', @type=N'LOCAL', @name=N'[Uncategorized (Local)]'
IF (@@ERROR &lt;&gt; 0 OR @ReturnCode &lt;&gt; 0) GOTO QuitWithRollback

END

DECLARE @jobId BINARY(16)
EXEC @ReturnCode =  msdb.dbo.sp_add_job @job_name=N'CmdExecTest', 
        @enabled=1, 
        @notify_level_eventlog=0, 
        @notify_level_email=0, 
        @notify_level_netsend=0, 
        @notify_level_page=0, 
        @delete_level=0, 
        @description=N'This job provides a way to test SQL Server Agent Jobs', 
        @category_name=N'[Uncategorized (Local)]', 
        @owner_login_name=N'&lt;me&gt;', @job_id = @jobId OUTPUT
IF (@@ERROR &lt;&gt; 0 OR @ReturnCode &lt;&gt; 0) GOTO QuitWithRollback
/****** Object:  Step [Step1]    Script Date: 2018-03-19 10:55:07 AM ******/
EXEC @ReturnCode = msdb.dbo.sp_add_jobstep @job_id=@jobId, @step_name=N'Step1', 
        @step_id=1, 
        @cmdexec_success_code=0, 
        @on_success_action=1, 
        @on_success_step_id=0, 
        @on_fail_action=2, 
        @on_fail_step_id=0, 
        @retry_attempts=0, 
        @retry_interval=0, 
        @os_run_priority=0, @subsystem=N'CmdExec', 
        @command=N'sqlcmd -E -S $(ESCAPE_SQUOTE(SRVR)) -d master -Q "EXECUTE [dbo].[DatabaseBackup] @Databases = ''USER_DATABASES'', @Directory = N''C:\Backup'', @BackupType = ''DIFF'', @Verify = ''Y'', @CleanupTime = NULL, @CheckSum = ''Y'', @LogToTable = ''Y''" -b', 
        @flags=32
IF (@@ERROR &lt;&gt; 0 OR @ReturnCode &lt;&gt; 0) GOTO QuitWithRollback
EXEC @ReturnCode = msdb.dbo.sp_update_job @job_id = @jobId, @start_step_id = 1
IF (@@ERROR &lt;&gt; 0 OR @ReturnCode &lt;&gt; 0) GOTO QuitWithRollback
EXEC @ReturnCode = msdb.dbo.sp_add_jobserver @job_id = @jobId, @server_name = N'(local)'
IF (@@ERROR &lt;&gt; 0 OR @ReturnCode &lt;&gt; 0) GOTO QuitWithRollback
COMMIT TRANSACTION
GOTO EndSave
QuitWithRollback:
    IF (@@TRANCOUNT &gt; 0) ROLLBACK TRANSACTION
EndSave:
GO


The result was a job failure for me because I don't have the dbo.DatabaseBackup stored procedure:

Msg 2812, Level 16, State 62, Server MyServer, Line 1
Could not find stored procedure 'dbo.DatabaseBackup'.

However, this indicates that sqlcmd was successfully executed.