FLC OF A MIL TRAINING ACFT HAD NMAC WITH ANOTHER ACFT WHILE CLBING IN VFR CONDITIONS.

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I WAS ON A ROUTINE TRAINING MISSION AT APPROX XX30 CLBING TO 17000 FT. IT WAS A HAZY MORNING WITH THE SUN LOW IN THE SKY; NO DISCERNABLE HORIZON. I HAD JUST TURNED TO AN E-NE HDG TO JOIN THE VICTOR AIRWAY. THE NOSE OF THE ACFT WAS SET AT APPROX 7 DEG NOSE HIGH. UPON REACHING 10000 FT; I LOOKED DOWN TO CHK MY OXYGEN SYS AND ASKED MY OTHER CREW MEMBERS TO CHK HIS; AS PER CHKLIST REQUIRES. WHEN I LOOKED UP; AN OBJECT APCHING MY R WING FROM FRONT TO REAR; CAUGHT MY ATTN. A QUICK GLANCE REVEALED A TWIN ENG ACFT PAINTED MOSTLY WHITE WITH 2 STRIPES: 1 LIGHT BLUE; 1 RED. THE PLT WAS WEARING A BLUE SHIRT AND HAD BLACK HAIR. MY ALT WAS APPROX 10100-10250 FT AND MY HDG WAS APPROX 075 DEGS. I CALLED DEP CTL TO RPT WHAT I SAW. THEY INDICATED A 'SHIN PAINT' BLIP 4 MI BEHIND MY ACFT. THEY HAD 'NEGATIVE RADIO CONTACT; NO FLT PLAN; AND NO XPONDER READOUT.' I FILED AN NMAC AND AM AWAITING THE FINAL RESULTS. I BELIEVE THE RAPCON CTLRS WEREN'T WATCHING THE SCREENS BECAUSE THEY WERE CAPABLE OF PICKING UP SHIN PAINT AFTER HE PASSED ME BUT NOT BEFORE. WHEN I FIRST INDICATED I HAD A NEAR MISS AND WANTED TO FILE A NMAC; THERE WAS A LONG PAUSE BEFORE I GOT A RESPONSE. IT'S EVERYONE'S RESPONSIBILITY TO CLR THEIR OWN FLT PATH BUT THERE ARE TIMES WHEN EVEN THAT IS NOT POSSIBLE. WITH THE SUN REFLECTING OFF OF MY ACFT AND THE SUN TO THE BACK OF THE WBOUND ACFT; IT'S DIFFICULT TO COME UP WITH A REASON FOR SUCH A CLOSE CALL.